BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Michael Shapiro
DTSTART:20230712T073000Z
DTEND:20230712T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/1
DESCRIPTION:Title: Symplectic groupoid and Teichmuller space of closed gen
us two curves (continued)\nby Michael Shapiro as part of Moscow-Beijin
g topology seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Kozlovskaya
DTSTART:20230719T073000Z
DTEND:20230719T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/2
DESCRIPTION:Title: Braid-like group. Simplicial structure on pure singular
braid groups.\nby Tatiana Kozlovskaya as part of Moscow-Beijing topol
ogy seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seokbeom Yoon
DTSTART:20230802T073000Z
DTEND:20230802T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/3
DESCRIPTION:Title: Super-Ptolemy coordinates and C^2-torsion polynomial\nby Seokbeom Yoon as part of Moscow-Beijing topology seminar\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20230809T073000Z
DTEND:20230809T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/4
DESCRIPTION:Title: Framed links in thickened surfaces and quantum invarian
ts of 3-manifolds with boundary\nby Eiji Ogasa as part of Moscow-Beiji
ng topology seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Sergeev
DTSTART:20230726T073000Z
DTEND:20230726T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/5
DESCRIPTION:Title: Pentagon Identity and Multidimensional Integrability\nby Sergei Sergeev as part of Moscow-Beijing topology seminar\n\nAbstrac
t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lin Jianfeng
DTSTART:20230816T073000Z
DTEND:20230816T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/6
DESCRIPTION:Title: Kontsevich's characteristic classes and formal smooth s
tructures\nby Lin Jianfeng as part of Moscow-Beijing topology seminar\
n\n\nAbstract\nIn 2018\, Watanabe disproved the 4-dimensional Smale conjec
ture by showing that the diffeomorphism group of a 4-dimensional disk rela
tive to its boundary is non-contractible. In Watanabe's proof he used a ve
rsion of Kontsevich's characteristic classes to detect non-trivial smooth
families of disk bundles. In this talk we will show that Kontsevich's char
acteristic classes only depend the formal smooth structure\, i.e. a lift o
f the tangent microbundle to a vector bundle. As an application\, we will
prove that for an arbitrary compact 4-manifold (with or without boundary)\
, the forgetful map from diffeomorphism group to the homeomorphism group i
s not a rational homotopy equivalence. And we will prove the same result f
or the 4-dimensional Euclidian space. This is joint work with Yi Xie (P
eking University)\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lin Dexie (Chongqing university)
DTSTART:20230823T073000Z
DTEND:20230823T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/7
DESCRIPTION:Title: Kodaira type conjecture on almost complex 4 manifolds\nby Lin Dexie (Chongqing university) as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nIn this paper\, we define a refined Dolbeault coho
mology on almost complex manifolds. We show that the condition h 1\,0 = h
˜0\,1 implies a symplectic structure on a compact almost complex 4 manifo
ld\, where ˜h 0\,1 is the Hodge number of the refined Dolbeault cohomolog
y and h 1\,0 is the Hodge number of the Dolbeault cohomology defined by Ci
rici and Wilson [5]. Moreover\, we prove that the condition h 1\,0 = h˜0\
,1 is equivalent to ∂∂¯-lemma\, which is similar to the case of compa
ct complex surfaces. Meanwhile\, unlike compact complex surfaces\, we show
that on compact almost complex 4 manifolds the equality b1 = h 0\,1 +h 1\
,0 does not hold in general.\nhttps://arxiv.org/pdf/2307.14690.pdf\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyu Yuan
DTSTART:20230830T073000Z
DTEND:20230830T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/8
DESCRIPTION:Title: Folded Morse trees and spectral networks\nby Tianyu
Yuan as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe present
an approach to do Morse theory on symmetric products of surfaces\, and sh
ow its relation to higher-dimensional Heegaard Floer homology (HDHF). As a
n application\, we recover the finite Hecke algebra by Morse theory. We al
so sketch the application to spectral networks. This is joint work with Ko
Honda and Yin Tian.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilshan Wijesena
DTSTART:20230906T073000Z
DTEND:20230906T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/9
DESCRIPTION:Title: Classifying representations of the Thompson groups and
the Cuntz algebra\nby Dilshan Wijesena as part of Moscow-Beijing topol
ogy seminar\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$ a
re one of the most remarkable discrete infinite groups for their several u
nusual properties. On the other hand\, the celebrated Cuntz algebra has ma
ny fascinating properties and it is known that $V$ embeds inside the Cuntz
algebra. However\, classifying the representations of the Thompson groups
and the Cuntz algebra have proven to be very difficult.\n\nLuckily\, than
ks to the novel technology of Vaughan Jones\, a rich family of so-called P
ythagorean representation of the Thompson groups and the Cuntz algebra can
be constructed by simply specifying a pair of finite-dimensional operator
s satisfying a certain equality. These representations carry a powerful di
agrammatic calculus which we use to develop techniques to study their prop
erties. This permits to reduce very difficult questions concerning irreduc
ibility and equivalence of infinite-dimensional representations into probl
ems in finite-dimensional linear algebra. Moreover\, we introduce the Pyth
agorean dimension which is a new invariant for all representations of the
Cuntz algebra. For each dimension $d$\, we show the irreducible classes fo
rm a moduli space of a real manifold of dimension $2d^2+1$. Finally\, we i
ntroduce the first known notion of a tensor product for representations of
the Cuntz algebra.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando (HSE University\, Skolkovo Institute of Science and T
echnology)
DTSTART:20230927T073000Z
DTEND:20230927T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/10
DESCRIPTION:Title: Weight systems related to Lie algebras\nby Sergei
Lando (HSE University\, Skolkovo Institute of Science and Technology) as p
art of Moscow-Beijing topology seminar\n\n\nAbstract\nPlease check the lin
k https://disk.yandex.ru/i/6D1IjHqHG6mYlA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Duzhin
DTSTART:20230913T073000Z
DTEND:20230913T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/11
DESCRIPTION:Title: On two practical problems of social choice theory\
nby Fedor Duzhin as part of Moscow-Beijing topology seminar\n\n\nAbstract\
nWe will introduce two practical problems in the social choice theory. \nT
he first scenario is envy-free division. Here\, n friends are renting an n
-bedroom apartment together. They need to split the rent and distribute th
e bedrooms among themselves so that everyone is happy with their bedroom\,
i.e.\, no one would prefer someone else's room to their own (given the re
nt). We will derive the existence of an envy-free division from Sperner's
Lemma (combinatorial analog of Brouwer's Fixed Point Theorem).\nThe second
scenario is peer evaluation. Here\, n students work on a common task\, an
d the job of the course instructor is to grade individual contributions to
group work. We assume that there exists an objective truth - a vector of
individual contributions that is known to students but not to the instruct
or. Students are required to do peer evaluation\, i.e.\, all team members
report their version of the truth. We will show then how the instructor ca
n design a method of grading that encourages students to report the truth
(the collective truth-telling is a strict Nash equilibrium).\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fengling Li
DTSTART:20230920T073000Z
DTEND:20230920T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/12
DESCRIPTION:Title: The $F$-polynomial invariant for knotoids\nby Feng
ling Li as part of Moscow-Beijing topology seminar\n\n\nAbstract\nAs a gen
eralization of the classical knots\, knotoids deal with the open ended kno
t diagram in a surface. \n\nIn recent years\, many polynomial invariants f
or knotoids appeared\, such as the bracket polynomial\, the index polynomi
al and the $n$th polynomial\, etc. \n\nIn this talk\, we introduce a new p
olynomial invariant $F$-polynomial for knotoids and discuss some propertie
s of it. This is joint work with Yi Feng.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akio Kawauchi (Osaka Central Advanced Mathematical Institute\, Osa
ka Metropolitan University)
DTSTART:20231004T073000Z
DTEND:20231004T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/13
DESCRIPTION:Title: Ribbon disk-link realization of contractible finite 2-
complex and Kervaire conjecture on group weight\nby Akio Kawauchi (Osa
ka Central Advanced Mathematical Institute\, Osaka Metropolitan University
) as part of Moscow-Beijing topology seminar\n\n\nAbstract\nKervaire conje
cture that the free product of every non-trivial group\nand the infinite c
yclic group is not normally generated by one element\nis confirmed. The id
ea is to solve Conjecture Z of a knot exterior proposed \nby F. Gonzalez-
Acuna and A. Ramirez as an equivalent conjecture. For this solution\,\na r
ibbon disk-link realization of a contractible finite 2-complex and the asp
hericity of\na ribbon disk-link are used.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dilshan Wijesena
DTSTART:20231025T073000Z
DTEND:20231025T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/14
DESCRIPTION:Title: Classifying representations of the Thompson groups and
the Cuntz algebra\nby Dilshan Wijesena as part of Moscow-Beijing topo
logy seminar\n\n\nAbstract\nRichard Thompson’s groups $F$\, $T$ and $V$
are one of the most remarkable discrete infinite groups for their several
unusual properties. On the other hand\, the celebrated Cuntz algebra has m
any fascinating properties and it is known that $V$ embeds inside the Cunt
z algebra. However\, classifying the representations of the Thompson group
s and the Cuntz algebra have proven to be very difficult.\n\nLuckily\, tha
nks to the novel technology of Vaughan Jones\, a rich family of so-called
Pythagorean representation of the Thompson groups and the Cuntz algebra ca
n be constructed by simply specifying a pair of finite-dimensional operato
rs satisfying a certain equality. These representations carry a powerful d
iagrammatic calculus which we use to develop techniques to study their pro
perties. This permits to reduce very difficult questions concerning irredu
cibility and equivalence of infinite-dimensional representations into prob
lems in finite-dimensional linear algebra. Moreover\, we introduce the Pyt
hagorean dimension which is a new invariant for all representations of the
Cuntz algebra. For each dimension $d$\, we show the irreducible classes f
orm a moduli space of a real manifold of dimension $2d^2+1$. Finally\, we
introduce the first known notion of a tensor product for representations o
f the Cuntz algebra.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20231011T073000Z
DTEND:20231011T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/15
DESCRIPTION:Title: Flat-virtual objects or how to map classical theory to
virtual theory\nby Vassily O. Manturov as part of Moscow-Beijing topo
logy seminar\n\n\nAbstract\nVirtual knot theory is a proper generalisation
of classical knot theory. It is known that virtual knots\nand links admit
many powerful invariants and techniques that never appeared in classical
knot theory.\n In the talk we construct a map from braids\, knots and link
s in the full torus to (closed relatives of) virtual\nbraids\, knots\, and
links.\n The talk is based on joint papers of the speaker with I.M.Nikono
v:\narXiv:2210.06862\narXiv:2210.09689\n Many unsolved problems will be s
tated. Many research projects will be formulated.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rhea Bakshi Palak
DTSTART:20231115T073000Z
DTEND:20231115T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/16
DESCRIPTION:Title: On the structure of the Kauffman bracket skein module<
/a>\nby Rhea Bakshi Palak as part of Moscow-Beijing topology seminar\n\n\n
Abstract\nSkein modules were introduced by Józef H. Przytycki as generali
sations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphe
re to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is t
he most extensively studied of all. However\, computing the KBSM of a 3-ma
nifold is known to be notoriously hard\, especially over the ring of Laure
nt polynomials. With the goal of finding a definite structure of the KBSM
over this ring\, several conjectures and theorems were stated over the yea
rs for KBSMs. We show that some of these conjectures\, and even theorems\,
are not true. In this talk I will briefly discuss a counterexample to Mar
che’s generalisation of Witten’s conjecture. I will show that a theore
m stated by Przytycki in 1999 about the KBSM of the connected sum of two h
andlebodies does not hold. I will also give the exact structure of the KBS
M of of the connected sum of two solid tori and show that it is isomorphic
to the KBSM of a genus two handlebody modulo some specific handle sliding
relations. Moreover\, these handle sliding relations can be written in te
rms of Chebyshev polynomials. I will also discuss the structure of the ske
in module of $S^1 \\times S^2 \\ \\# \\ H_1$ and $S^1 \\times S^2 \\ \\# \
\ S^1 \\times S^2$. Parts of this talk are based on joint work with Thang
Le\, Józef Przytycki\, Seongjeong Kim\, and Xiao Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20231122T053000Z
DTEND:20231122T070000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/18
DESCRIPTION:Title: Distance formulas for any four points on a plane. Poss
ible applications to pentagon case\nby Hayk Sedrakyan as part of Mosco
w-Beijing topology seminar\n\n\nAbstract\nGiven a connected graph with fou
r vertices and six edges (a quadrilateral and its diagonals). We obtained
a novel formula to find the length of any of its edges using the other fiv
e edge lengths. We are interested in possible applications of this formula
to pentagon case.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haimiao Chen
DTSTART:20231206T073000Z
DTEND:20231206T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/19
DESCRIPTION:Title: Torsion in the skein module of the complement of a 4-s
trand Montesinos knot\nby Haimiao Chen as part of Moscow-Beijing topol
ogy seminar\n\n\nAbstract\nFor a 3-manifold M\, let S(M) denote its Kauffm
an bracket skein module. Problem 1.92 (G) (i) in the Kirby's list asks whe
ther S(M) is free when M is irreducible and has no incompressible non-para
llel to the boundary torus. We answer this negatively by showing that S(M)
contains torsion when M is the complement of a 4-strand Montesinos knot i
n the 3-sphere.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Yakovlevich Kanel-Belov
DTSTART:20231213T073000Z
DTEND:20231213T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/20
DESCRIPTION:Title: Quantization\, polynomial automorphisms and the Jacobi
an problem.\nby Alexey Yakovlevich Kanel-Belov as part of Moscow-Beiji
ng topology seminar\n\n\nAbstract\nLet F: Cn→ Cn be a polynomial mapping
of a complex space into itself. When is it reversible? A necessary condit
ion is local invertibility at each point. The famous Jacobian problem stat
es that this condition is sufficient. For more than 20 years\, until 1968\
, the Jacobian problem was considered solved for n = 2\, since then new
“evidence” has appeared every few months.\n\nThe Jacobian problem is c
losely related to the Dixmier conjecture\, the formulation of which for n=
1 looks innocent: let P\, Q be polynomials in x and (d/dx)\, and PQ– QP=
1. Is it true that (d/dx) can be expressed in terms of P and Q. This state
ment has not yet been proven. Recently it was possible to prove the equiva
lence of this statement to the Jacobian problem for n=2. The stable equiva
lence of the Jacobian and Dixmier conjectures is proven in the work http:/
/arxiv.org/abs/math/0512171. The proof uses an analogy between classical a
nd quantum objects. It is intended to give an elementary explanation of th
is analogy and also discuss Kontsevich’s hypotheses.\n\nAnother\, close\
, statement is called the Abiencar–Moch theorem and looks like an Olympi
ad problem (which it is). Let P\, Q\, R be polynomials\, and R(P(x)\,Q(x))
=x. Prove that either the degree of P divides the degree of Q\, or vice ve
rsa.\n\nThe first part of the report is an introduction to the problem and
is supposed to be quite elementary\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily Olegovich Manturov
DTSTART:20231220T073000Z
DTEND:20231220T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/21
DESCRIPTION:Title: A map from classical theory to virtual knot theory. An
introduction to flat-virtual knots\nby Vassily Olegovich Manturov as
part of Moscow-Beijing topology seminar\n\n\nAbstract\nProfessor Manturov
will talk in more detail about two constructions suggested in the papers h
ttps://arxiv.org/abs/2210.06862\, https://arxiv.org/abs/2210.09689 where c
lassical objects (classical braid\, knots in the full torus and knots in
the thickened torus) are mapped analogues of virtual knots: the so-called
flat-virtual knots. Professor Manturov will discuss various invariants of
the latter leading to lots of invariants of classical objects\, generalis
ing the Burau representation\, Kauffman bracket\, and many other objects.
Many unsolved problems will be formulated during the talk.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Xiaoyang
DTSTART:20240103T073000Z
DTEND:20240103T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/22
DESCRIPTION:Title: Rational ellipticity of Riemannian manifolds\nby C
hen Xiaoyang as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIt
was conjectured by Bott-Grove-Halperin that a compact simply connected Rie
mannian manifold with nonnegative sectional curvature is rationally ellipt
ic\, i.e.\, it has finite dimensional rational homotopy groups. We will di
scuss some recent progress on this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ren Shiquan
DTSTART:20231227T073000Z
DTEND:20231227T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/23
DESCRIPTION:Title: Regular maps on Cartesian products and disjoint unions
of manifolds\nby Ren Shiquan as part of Moscow-Beijing topology semin
ar\n\n\nAbstract\nA map from a manifold to a Euclidean space is said to be
k-regular if the images of any distinct k points are linearly independent
. For k-regular maps on manifolds\, lower bounds on the dimension of the a
mbient Euclidean space have been extensively studied. In this talk\, we st
udy the lower bounds on the dimension of the ambient Euclidean space for 2
-regular maps on Cartesian products of manifolds. As corollaries\, we obta
in the exact lower bounds on the dimension of the ambient Euclidean space
for 2-regular maps and 3-regular maps on spheres as well as on some real p
rojective spaces. Moreover\, generalizing the notion of k-regular maps\, w
e study the lower bounds on the dimension of the ambient Euclidean space f
or maps with certain non-degeneracy conditions from disjoint unions of man
ifolds into Euclidean spaces.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Dobritsyn
DTSTART:20240110T073000Z
DTEND:20240110T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/24
DESCRIPTION:by Mikhail Dobritsyn as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nThe van der Waerden’s theorem is an important result in
combinatorics of arithmetic progressions. It turns out\, this theorem is
easily solvable in agame from and winning strategy requires much fewer mov
es to win.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyun Cheng
DTSTART:20240117T073000Z
DTEND:20240117T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/25
DESCRIPTION:Title: The calculation of the rank of the incidence matrix of
a hypergraph\nby Zhiyun Cheng as part of Moscow-Beijing topology semi
nar\n\n\nAbstract\nIn this talk\, I will explain how to calculate the rank
of the incidence matrix of a hypergraph. Several concrete examples will b
e discussed.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhang Zhi-Hao
DTSTART:20240124T073000Z
DTEND:20240124T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/26
DESCRIPTION:Title: Enriched categories and their centers\nby Zhang Zh
i-Hao as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe notion
of an enriched (fusion) category naturally appears in the study of the ma
thematical theory of topological orders. In this talk\, I will introduce a
symmetric monoidal 2-category of enriched categories with arbitrary backg
round categories. Then the notion of an enriched (braided or symmetric) mo
noidal category can be defined as an E_n-algebra in this 2-category. Final
ly I will introduce the notion of a center and compute the center of an en
riched (monoidal or braided monoidal) category. This talk is based on a jo
int work arXiv:2104.03121 with Liang Kong\, Wei Yuan and Hao Zheng.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Dmitrievich Mednykh
DTSTART:20240131T073000Z
DTEND:20240131T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/27
DESCRIPTION:Title: Spectral Invariants of Graphs and Their Applications t
o Combinatorics.\nby Alexander Dmitrievich Mednykh as part of Moscow-B
eijing topology seminar\n\n\nAbstract\nWe present recent results obtained
by the authors. They are related to spectral invariants of graphs admittin
g an arbitrary large cyclic group action. To illustrate them we use the fa
mily of circulant graphs G_n = C_n(s_1\, s_2\, . . . \, s_k). The Chebyshe
v polynomials provide a significant analytical tools for studying the prop
erties of such graphs and their characteristic polynomials. In particular\
, this gives a way to find analytical expressions for the number of spanni
ng trees τ(n)\, the number of rooted spanning forests f_{G}(n) and the Ki
rchhoff index Kf(G_n) of a graph. We are interested in the behaviour of th
ese invariants for sufficiently large n. We provide asymptotic formulas of
the above mentioned invariants. These results were motivated by problems
arising in theoretical physics\, biology and chemistry.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kodai Wada (Kobe University)
DTSTART:20240207T073000Z
DTEND:20240207T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/28
DESCRIPTION:Title: Virtualized Delta moves for virtual knots and links\nby Kodai Wada (Kobe University) as part of Moscow-Beijing topology semi
nar\n\n\nAbstract\nWe introduce a local deformation called a virtualized D
elta move for unoriented virtual knots and links. We prove that it is an u
nknotting operation for unoriented virtual knots\, and give a necessary an
d sufficient condition for two unoriented virtual links of two or more com
ponents to be related by a finite sequence of virtualized Delta moves. We
also talk about virtualized Delta\, sharp\, and pass moves for oriented vi
rtual knots and links. This is a joint work with Takuji Nakamura\, Yasutak
a Nakanishi\, and Shin Satoh.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando
DTSTART:20240221T073000Z
DTEND:20240221T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/29
DESCRIPTION:Title: Inducing graph invariants from the universal $\\mathca
l{gl}$-weight system\nby Sergei Lando as part of Moscow-Beijing topolo
gy seminar\n\n\nAbstract\nWeight systems\, which are functions on chord di
agrams satisfying certain 4-term relations\, appear naturally in Vassiliev
's theory of nite type knot invariants.\nIn particular\, a weight syste
m can be constructed from any nite dimensional\nLie algebra endowed wit
h a nondegenerate invariant bilinear form. Recently\,\nM. Kazarian suggest
ed to extend the $gl(N)$-weight system from chord diagrams\n(treated as in
volutions without xed point) to arbitrary permutations\, which\nled to
a recurrence formula allowing for an e ective computation of its values\
,\nelaborated by Zhuoke Yang. In turn\, the recurrence helped to unify the
$\\mathcal{gl}(N)$\nweight systems\, for $N = 1\, 2\, 3\,\\dots$\, into a
universal gl-weight system. The\nlatter takes values in the ring of polyn
omials $\\mathbb{C}[N][C_1\,C_2\,\\dots]$ in in nitely many variables $C
_1\,C_2\,\\dots$ (Casimir elements)\, whose coe cients are polynomials i
n $N$.\nThe universal $\\mathcal{gl}$-weight system carries a lot of infor
mation about chord\ndiagrams and intersection graphs. The talk will addres
s the question which graph\ninvariants can be extracted from it. We will d
iscuss the interlace polynomial\,\nthe enhanced skew-characteristic polyno
mial\, and the chromatic polynomial. In\nparticular\, we show that the int
erlace polynomial of the intersection graphs can\nbe obtained by a speci
c substitution for the variables $n\,C_1\,C_2\,\\dots$. This allows\non
e to extend it from chord diagrams to arbitrary permutations.\nQuestions c
oncerning other graph and delta-matroid invariants and their\npresumable e
xtensions will be formulated.\nThe talk is based on a work of the speaker
and a PhD student Nadezhda\nKodaneva.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240228T073000Z
DTEND:20240228T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/30
DESCRIPTION:Title: Knot in $S_{g}\\times S^{1}$ of degree one and long kn
ot invariants\nby Seongjeong Kim as part of Moscow-Beijing topology se
minar\n\n\nAbstract\nIn this talk we construct invariants for knots in $S_
{g}\\times S^{1}$ of degree one by using long knot invariants.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiang Yi
DTSTART:20240320T073000Z
DTEND:20240320T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/32
DESCRIPTION:Title: Free circle actions on highly connected (2n+1)-manifol
ds\nby Jiang Yi as part of Moscow-Beijing topology seminar\n\n\nAbstra
ct\nA natural problem in topology is to determine which manifolds admit ce
rtain group actions. The problem we concern in this talk is to determine w
hich highly connected (2n+1)-manifolds admit free circle actions. I will i
ntroduce some previous work and our progress on this problem. This is a jo
int work with Yang Su.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirova Valeriia
DTSTART:20240306T073000Z
DTEND:20240306T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/33
DESCRIPTION:Title: On the combinatorial complexity functions of Sturmian
words\nby Kirova Valeriia as part of Moscow-Beijing topology seminar\n
\n\nAbstract\nConsider combinatorial complexity functions of infinite word
s\, especially factor complexity and its modifications. First of all\, we
present an overview of the available results for Sturmian words. Special a
ttention is paid to the arithmetical complexity of infinite words\, the st
udy of which was initiated by Van der Waarden Theorem on one-color arithme
tic progressions. Arithmetical complexity is presented in a sense a modifi
cation of factor complexity. An overview of current results and exact val
ues of arithmetic complexity for Sturmian words is presented. We present p
olynomial Van der Waerden Theorem\, which gives rise to the study of a mo
re generalized modification of the factor complexity function - the polyno
mial complexity of infinite words.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco De Renzi
DTSTART:20240403T073000Z
DTEND:20240403T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/34
DESCRIPTION:Title: Homological and quantum representations of mapping cla
ss groups\nby Marco De Renzi as part of Moscow-Beijing topology semina
r\n\n\nAbstract\nFor a connected surface Σ with connected boundary\, ther
e exist two very different constructions of the same family of representat
ions of the mapping class group Mod(Σ): one comes from the non-semisimple
TQFT associated with the quantum group of sl(2)\, while the other arises
from twisted homology groups of configuration spaces of Σ. I will expla
in the equivalence between the two actions\, and how this is expected to g
eneralize in the presence of cohomology classes. This is based on joint wo
rks with Jules Martel and Bangxin Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Baptiste Meilhan
DTSTART:20240313T073000Z
DTEND:20240313T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/35
DESCRIPTION:Title: Cut-diagrams and surfaces in 4-space\nby Jean-Bapt
iste Meilhan as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe
purpose of this talk is to define a family of (concordance and link-homot
opy) invariants of knotted surfaces in 4-space. The construction is modele
d on Milnor link invariants\, which are numerical concordance invariants o
f links in 3-space\, extracted from the nilpotent quotients of the link gr
oup. Our construction makes use of "cut-diagrams" of knotted surfaces in 4
-space\, which encode these objects in a simple combinatorial way. Roughly
speaking\, for a knotted surface obtained as embedding of the abstract su
rface S\, a cut-diagram is a kind of 1-dimensional diagram on S with some
labeling. We will provide several examples and applications. No expertise
in 4-dimensional topology is required for this talk. This is a joint work
with Benjamin Audoux and Akira Yasuhara.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramanujan Santharoubane
DTSTART:20240410T073000Z
DTEND:20240410T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/36
DESCRIPTION:Title: An embedding of the Kauffman bracket skein algebra of
a surface into a localized quantum torus\nby Ramanujan Santharoubane a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nI will explain ho
w to build a new embedding of the Kauffman bracket skein algebra of a surf
ace into a localized quantum torus via Dehn-Thurston coordinates. The quan
tum torus is said to be localized because certain extra elements need to b
e inverted. An important property is that the localized quantum torus is s
omehow a finite extension of the skein algebra. As an application I will s
how how to recover a proof of the unicity conjecture already proved by Fro
hman\, Kania-Bartoszynska and Lê. An explicit description of most irreduc
ible representations of the skein algebra at root of unity will be possibl
e.\nThis is joint work with Renaud Detcherry.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoît Guerville-Ballé
DTSTART:20240327T073000Z
DTEND:20240327T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/37
DESCRIPTION:Title: Connectedness and combinatorial interplay in the modul
i space of line arrangements.\nby Benoît Guerville-Ballé as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nThe moduli space of a line
arrangement (also known as the realization space) captures important topol
ogical and geometric information about the arrangement. Due to Mnëv’s U
niversality Theorem\, such moduli spaces can behave as wild as one can ima
gine. Furthermore\, the Pappus configuration shows that unexpected colline
arity can appear among the singular points of an arrangements. In this tal
k\, and despite these results\, we focus on extracting topological informa
tion on the moduli space of line arrangements using only combinatorial tec
hniques. In the first part\, we investigate the combinatorial class of ind
uctively connected line arrangements defined by Nazir and Yoshinaga. These
arrangements are characterized by a recursive structure that ensures thei
r moduli space to be an open Zariski subset of an irreducible algebraic va
riety\, and so to be path-connected. The second part will be devoted to a
continuation of their work. For any fixed line arrangement\, we inductivel
y compute a combinatorial upper-bound of the number of connected component
s of the moduli space. Our bound is based on a fine study of the equations
governing the incidence relations\, and more particularly of their degree
s. It is shown to be sharp even for moduli space with an arbitrary large n
umber of connected components. This is a joint work with Juan Viu-Sos.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Audoux
DTSTART:20240515T073000Z
DTEND:20240515T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/38
DESCRIPTION:Title: Welded graphs\, Wirtinger presentations and knotted pu
nctured spheres\nby Benjamin Audoux as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nIn this talk\, I will introduce welded graphs\, th
at can be seen as combinatorial objects lying between 3-dimensional knots
and 4-dimensional knotted surfaces. For these objects\, I will define a no
tion of peripheral system from which I will extract Milnor invariants. Thi
s will lead to a complete classification of knotted punctured spheres (wit
h trivially embedded boundary) up to link-homotopy.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Hass
DTSTART:20240417T073000Z
DTEND:20240417T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/39
DESCRIPTION:Title: Knotted surfaces and their profile curves\nby Joel
Hass as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe profil
e curve of a surface in R3 is formed from the points whose tangent plane i
s vertical. This is the "outline" of a surface. When a surface is transp
arent\, this curve is what is most visible to the eye. Profile curves pla
y a role in surface reconstruction\, the problem of reconstructing a surfa
ce from photographs. In this talk I will investigate the relationship betw
een the knot type of a profile curve and that of the surface it lies on.
For example\, I will answer the following question: Is there an unknotted
torus whose profile curves contain a component that is the standard trefo
il knot?\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruben Louis
DTSTART:20240424T073000Z
DTEND:20240424T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/40
DESCRIPTION:Title: On Nash resolution of (singular) Lie algebroids\nb
y Ruben Louis as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe
show that any Lie algebroid A admits a Nash-type blow-up Nash(A) that sit
s in a nice short exact sequence of Lie algebroids 0–>K–>p*A–>D–>0
with K a Lie algebra bundle and D a Lie algebroid whose anchor map is inj
ective on an open dense subset. The base variety is a blowup determined by
the singular foliation of A. We provide concrete examples. Moreover\, we
extend the construction following Mohsen’s to singular subalgebroids in
the sense of Androulidakis-Zambon.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingying Deng
DTSTART:20240522T073000Z
DTEND:20240522T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/41
DESCRIPTION:Title: Partial-dual polynomial as a framed weight system\
nby Qingying Deng as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nRecently\, Chmutov proved that the partial-dual polynomial considered as
a function on chord diagrams satisfies the four-term relation. In this ta
lk\, I will introduce two generalization results about it (Communications
in Mathematics 31 (2023)\, no. 3\, 151–160\, and arXiv:2404.10216).\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarita Shevtsova\, Ivan Vorobiev
DTSTART:20240501T073000Z
DTEND:20240501T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/42
DESCRIPTION:Title: Symbolic dynamics\, First and Second digits of sequenc
es\nby Margarita Shevtsova\, Ivan Vorobiev as part of Moscow-Beijing t
opology seminar\n\n\nAbstract\nThe talk will be devoted to an introduction
to the word theory and the description of several problems that it is con
cerned with. We will call a ”word” an infinite sequence of symbols tha
t is generated from a dynamical system.$M$ --- a compact metric space$U$ -
-- open subspace of M$f : M \\rightarrow M$ is a homeomorphism of the comp
act into itself$x_0 \\in M$ — an initial point. It determine{s a sequenc
e of symbols\n\n$$\n\nw_n = \\begin{cases} a\, f^{(n)}(x_0)\\in U \\\\ b\,
f^{(n)}(x_0)\\not \\in U \\end{cases}\n\n$$\n\nWe will be investigating t
he different combinations of m consecutive symbols (”subwords”) that c
an be found in such words depending on which dynamic system was used to ge
nerate them. We will be looking at the famous Sturmian sequences\, some of
their generalizations and their Rauzy graphs in more detail. Several dyna
mic systems and their implications will be discussed in more detail. Namel
y\, circle rotation\, interval exchange transformation\, billiards\, the f
irst digit of $2^n$\, $n!$\, $2^{n^2}$ \, the second digit of $2^n$.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20240731T073000Z
DTEND:20240731T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/43
DESCRIPTION:Title: Seifert surfaces for virtual knots\nby Eiji Ogasa
as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe introduce Sei
fert surfaces for virtual knots.\nVirtual knots are represented by knots i
n thickened oriented surfaces\,\nwhich may be a non-zero cycle. Although i
t may be a non-zero cycle\,\nwe can define Seifert surfaces for virtual kn
ots.\n We also define Seifert matrices associated with our new Seifert su
rfaces.\nFurthermore\, by using our new Seifert matrices\,\nwe introduce t
he Alexander polynomials and the signature.\n Our Alexander polynomial
of virtual knots can obstruct from being classical knots.It is mirror sens
itive as isotopy invariants.\n Our signature is mirror sensitive as diffe
omorphic invariants.\nThis talk is based on the paper\,\n New invariants
for virtual knots via spanning surfaces\nJournal of knot theory and its ra
mifications 2024 arXiv:2207.08129 [math.GT]\nwritten by András Juhász\,
Louis H. Kauffman\, and the speaker.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shen Dawei
DTSTART:20240508T073000Z
DTEND:20240508T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/44
DESCRIPTION:Title: The magnitude for algebras is a generalization of the
Euler characteristic\nby Shen Dawei as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nWe investigate the magnitude for Nakayama algebras
. Using Ringel’s resolution quiver\, the existence and the value of rati
onal magnitude is given. As a result\, we show directly that two finite gl
obal dimension criteria for Nakayama algebras are equivalent. This is a jo
int work with Yaru Wu.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20240529T073000Z
DTEND:20240529T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/45
DESCRIPTION:Title: Novel Sedrakyan-Mozayeni theorem\, and its application
s in scientific research in topology and geometry\nby Hayk Sedrakyan a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this presentat
ion\, we consider several applications of the Sedrakyan-Mozayeni theorem.
In particular\, we investigate how it can be applied in novel mathematical
scientific research in topology and geometry to generalize the pentagon c
ase of the photography principle\, data transmission and invariants of man
ifolds. We will also go in depth on the derivation of Sedrakyan-Mozayeni t
heorem\, and explain current issues with the pentagon case of the photogra
phy principle. Besides having theoretical applications\, the formula can b
e used in applied mathematics and lead to new real-world results. We will
implement the formula into a code and generate several computer simulation
s applied in novel mathematical scientific research in topology and geomet
ry.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darya Popova
DTSTART:20240612T073000Z
DTEND:20240612T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/46
DESCRIPTION:Title: Flat virtual links and knot invariants\nby Darya P
opova as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn the tal
k I will review a way of constructing invariants of knots in S^3\, thicken
ed torus and thickened cylinder that was introduced by V. O. Manturov and
I. M. Nikonov. The idea is to map the knots to flat virtual diagrams and u
se invariants of flat virtual diagrams. Besides I will talk about my findi
ngs on the diagrams which we get by this approach and how they lead to a h
ypothesis that the potential of this approach for getting very strong inva
riants of knots is small.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (YMSC)
DTSTART:20240626T073000Z
DTEND:20240626T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/47
DESCRIPTION:Title: Moduli spaces of quadratic differentials: Abel-Jacobi
maps and deformation\nby Yu Qiu (YMSC) as part of Moscow-Beijing topol
ogy seminar\n\n\nAbstract\nWe give correspondences between: 1. deformation
of 3-Calabi-Yau categories\; 2. partial compactification with orbifolding
of moduli spaces and 3. taking sub-quotient of mapping class groups.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Nilov
DTSTART:20240605T073000Z
DTEND:20240605T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/48
DESCRIPTION:Title: Webs from circles and lines\nby Fedor Nilov as par
t of Moscow-Beijing topology seminar\n\n\nAbstract\nWe give an overview of
known results related to webs from circles and lines in Blaschke-Bol prob
lem and discuss an idea to construct some new examples.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Wu
DTSTART:20240814T073000Z
DTEND:20240814T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/50
DESCRIPTION:Title: Applications of GLMY theory in metabolomic networks of
complex diseases\nby Shuang Wu as part of Moscow-Beijing topology sem
inar\n\n\nAbstract\nHuman diseases involve metabolic alterations. Metabolo
mic profiles have served as a biomarker for the early identification of hi
gh-risk individuals and disease prevention. However\, current approaches c
an only characterize individual key metabolites\, without taking into acco
unt their interactions.This work have leveraged a statistical physics mode
l to combine all metabolites into bDSW networks and implement GLMY homolog
y theory to analyze and interpret the topological change of health state f
rom symbiosis to dysbiosis.The application of this model to real data allo
ws us to identify several hub metabolites and their interaction webs\, whi
ch play a part in the formation of inflammatory bowel diseases.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fu
DTSTART:20240619T073000Z
DTEND:20240619T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/51
DESCRIPTION:Title: Cohomology of partial quotients\nby Xin Fu as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nBuchstaber and Panov in
troduced the notion of the moment-angle complex Z. This space is defined a
s a union of specific product spaces of discs and circles\, equipped with
a natural action of a torus T. Topologically\, a moment-angle complex prov
ides a way to understand a simplicial toric variety through its quotient Z
/H\, where H is a closed subgroup of T. The computation of the cohomology
groups and cup products for these quotient spaces involves techniques from
combinatorics\, algebra\, and homotopy theory. These techniques have appl
ications in various fields. This talk summarizes known results for computi
ng such cohomology and presents our new progress. Our new approach uses di
graphs to describe the weights that encode how the torus is twisted in the
quotient space.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Shapiro
DTSTART:20240703T073000Z
DTEND:20240703T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/52
DESCRIPTION:Title: Mystery of point charges after Gauss-Maxwell-Morse
\nby Boris Shapiro as part of Moscow-Beijing topology seminar\n\n\nAbstrac
t\nIn his 2 volume chef-d'oeuvre “Treatise of electricity and Magnetism
” J.C.Maxwell (among thousands of much more important claims) formulated
the following statement.\n\nGiven any configurations of N fixed point cha
rges in R^3\, the electrostatic field created by them has at most (N-1)^2
points of equilibrium.\n\nMaxwell’s arguments are incomplete and this pr
oblem was considered much later by M.Morse and revitalised about two decad
es ago. However Maxwell’s original claim is still open already in case o
f N=3 charges. In my talk I will survey what is known in this direction an
d\, in particular\, formulate a calculus 1 problem which currently still r
emains unsolved.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yurii Belov
DTSTART:20240710T073000Z
DTEND:20240710T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/53
DESCRIPTION:Title: Spectral synthesis for systems of exponentials and rep
roducing kernels\nby Yurii Belov as part of Moscow-Beijing topology se
minar\n\n\nAbstract\nLet $x_n$ be a complete and minimal system of vectors
in a Hilbert space $H$. We say\nthat this system is hereditarily complete
or admits spectral synthesis if any vector in $H$\ncan be approximated in
the norm by linear combinations of partial sums of the Fourier\nseries wi
th respect to $x_n$. It was a long-standing problem whether any complete a
nd\nminimal system of exponentials in $L^2(-a\,a)$ admits spectral synthes
is. Several years ago\nA. Baranov\, A. Borichev and myself managed to give
a negative answer to this question which implies\,\nin particular\, that
there exist non-harmonic Fourier series which do not admit a linear\nsumma
tion method. We also showed that any exponential system admits the\nsynthe
sis up to a one-dimensional defect. Apart from this\, I will discuss relat
ed problems\nfor systems of reproducing kernels in Hilbert spaces of entir
e functions. In particular\,\nI will talk about a counterexample to the Ne
wman-Shapiro conjecture posed in 1966 \n(joint work with A. Borichev).\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilong Wang
DTSTART:20240828T073000Z
DTEND:20240828T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/54
DESCRIPTION:Title: Alterfold invariants and alterfold TQFT\nby Yilong
Wang as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn this ta
lk\, we introduce the notion of alterfold invariants and their associated
TQFTs. Then we will give several applications including the topological de
scription of the Drinfeld center\, the equivalence between the RT- and TV-
TQFTs\, and the equivariance of the generalized Frobenius-Schur indicators
. Finally\, we will discuss how to obtain families of Morita invariants as
generalizations of the indicators\, and speculate some of the potential a
pplications. This is based on joint work with Zhengwei Liu\, Shuang Ming a
nd Jinsong Wu.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadiy Skopenkov
DTSTART:20240821T073000Z
DTEND:20240821T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/55
DESCRIPTION:Title: The band connected sum and the second Kirby move for h
igher-dimensional links\nby Arkadiy Skopenkov as part of Moscow-Beijin
g topology seminar\n\n\nAbstract\nLet $f:S^q\\sqcup S^q\\to S^m$ be an (or
dered oriented) link (i.e. an embedding).\n\nHow does (the isotopy class o
f) the knot $S^q\\to S^m$ obtained by embedded connected sum of the compon
ents of $f$ depend on $f$?\n\nDefine a link $\\sigma f:S^q\\sqcup S^q\\to
S^m$ as follows.\nThe first component of $\\sigma f$ is the `standardly sh
ifted' first component of $f$.\nThe second component of $\\sigma f$ is the
embedded connected sum of the components of $f$.\nHow does (the isotopy c
lass of) $\\sigma f$ depend on $f$?\n\nHow does (the isotopy class of) the
link $S^q\\sqcup S^q\\to S^m$ obtained by embedded connected sum of the l
ast two components of a link $g:S^q_1\\sqcup S^q_2\\sqcup S^q_3\\to S^m$ d
epend on $g$?\n\nWe give the answers for the `first non-trivial case' $q=4
k-1$ and $m=6k$.\nThe first answer was used by S. Avvakumov for classifica
tion of linked 3-manifolds in $S^6$.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Ming (BIMSA)
DTSTART:20240807T073000Z
DTEND:20240807T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/56
DESCRIPTION:Title: Tensor categories and alterfold theory\nby Shuang
Ming (BIMSA) as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn
this talk\, I will introduce a partition function defined on bi-colored th
ree-manifolds decorated by tensor diagrams from a spherical fusion categor
y \\mathcal{C}. We called them 3 dimensional alterfold. This partition fun
ction yields three-manifold invariants and three-dimensional topological q
uantum field theories (TQFTs). I will discuss how well-known invariants an
d TQFTs\, such as Turaev-Viro theory and Reshetikhin-Turaev theory\, can b
e naturally embedded within our framework. Furthermore\, our bi-colored th
eory provides topological interpretations for fundamental concepts in tens
or categories\, including the Drinfeld center and Frobenius-Schur indicato
rs. We expect the theory could generalizes to higher dimensions\, and coul
d produce new identities for (higher) tensor categories.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengwei Liu
DTSTART:20240911T073000Z
DTEND:20240911T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/57
DESCRIPTION:by Zhengwei Liu as part of Moscow-Beijing topology seminar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Wu
DTSTART:20241009T073000Z
DTEND:20241009T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/58
DESCRIPTION:Title: Topology meets Artificial Intelligence (AI)\nby Ji
e Wu as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThis talk a
ims to address one of the fundamental questions in the mind of youngth wha
t we (as topologists or pre-topologists) could/should do in the times of A
rtificial Intelligence (AI). For helping you to find the answer of this qu
estion that is suitable to yourself\, we will talk by samples on the bi-di
rectional interactions between algebraic topology and AI\, which consists
of an introduction to a work of Kirill Brilliantov\, Fedor Pavutniskiy\, D
mitry Pasechnyuk and German Magao on the applications of language models t
o some hard problems in algebraic topology\, a new-born research field of
GLMY theory on digraphs that aims to establish topological foundations for
high-order interaction complex network\, and some practical applications
of algebraic topology in sciences.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bing Fang (Dalian University of Technology)
DTSTART:20240904T073000Z
DTEND:20240904T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/59
DESCRIPTION:Title: Sufficient conditions for amalgamated 3-manifolds to b
e $\\partial$-irreducible and irreducible\nby Bing Fang (Dalian Univer
sity of Technology) as part of Moscow-Beijing topology seminar\n\n\nAbstra
ct\nLet $M=M_1\\cup_F M_2$ be an amalgamation of two 3-manifolds $M_1$ and
$M_2$ along a compact connected surface $F$. In this talk\, we first give
some sufficient conditions for $M$ to be $\\partial$-irreducible in terms
of distances between certain vertex subsets of the curve complex $C(F)$ a
nd the arc complex $A(F)$. Then we introduce the extended curve complex $\
\widetilde{C}(F)$ of a compact connected surface $F$. In the case that $F$
is bi-compressible in the amalgamated 3-manifold $M$ and in the case that
$F$ is compressible only in one of $M_1$ and $M_2$\, we give some suffici
ent conditions in terms of distance between some vertex subsets of $\\wide
tilde{C}(F)$ for $M$ to be irreducible\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Verelzier
DTSTART:20241002T073000Z
DTEND:20241002T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/60
DESCRIPTION:Title: State sum homotopy invariants of maps\nby Alexis V
erelzier as part of Moscow-Beijing topology seminar\n\n\nAbstract\nHomotop
y quantum field theories (HQFTs) generalize topological quantum field theo
ries (TQFTs). The idea is to use TQFT techniques to study principal fiber
bundles over manifolds and\, more generally\, homotopy classes of maps fro
m manifolds to a fixed target space X. In particular\, such an HQFT induce
s a scalar invariant of homotopy classes of maps from closed manifolds to
X. It is well-known that groups are algebraic models for 1-types. Generali
zing groups\, crossed modules model 2-types. In this talk\, I will explain
how to generalize the Turaev-Viro-Barett-Westburry state sum method to de
fine a 3-dimensional HQFT with target X in the following two cases: first
when X is a 1-type using fusion categories graded by a group (joint work w
ith Vladimir Turaev) and second when X is a 2-type using fusion categories
graded by a crossed module (joint work with Kursat Sozer).\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liliya Grunwald
DTSTART:20240918T073000Z
DTEND:20240918T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/61
DESCRIPTION:Title: Аналитическая теория циркуля
нтных графов и ее приложения к комбинато
рному анализу\nby Liliya Grunwald as part of Moscow-Beijin
g topology seminar\n\n\nAbstract\nДоклад посвящен изуче
нию актуальных вопросов современного ан
ализа\, которые находятся на стыке компл
ексного анализа\, комбинаторного анализ
а\, теории графов и алгебры. В работе расс
матриваются спектральные и алгебраичес
кие свойства дискретного лапласиана\, пр
именительно к широкому семейству циркул
янтных графов и их различных обобщений.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240925T073000Z
DTEND:20240925T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/62
DESCRIPTION:Title: Classification of knots in $S_{g} \\times S^{1}$ with
small number of crossings\nby Seongjeong Kim as part of Moscow-Beijing
topology seminar\n\n\nAbstract\nIn knot theory not only classical knots\,
which are embedded circles in S^{3} up to isotopy\, but also knots in oth
er 3-manifolds are interesting for mathematicians. In particular\, virtual
knots\, which are knots in thickened surface $S_{g} \\times [0\,1]$ with
an orientable surface $S_{g}$ of genus $g$\, are studied and they provide
interesting properties.\n\nIn this talk\, we will talk about knots in $S_{
g} \\times S^{1}$ where $S_{g}$ is an oriented surface of genus $g$. We in
troduce basic notions and properties for them. In particular\, for knots i
n $S_{g} \\times S^{1}$ one of important information is “how many times
a half ot a crossing turns around $S^{1}$”\, and we call it winding pari
ty of a crossing. We extend this notion more generally and introduce a top
ological model. In the end we apply it to classify knots in $S_{g}\\times
S^{1}$ with small number of crossings.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng Du
DTSTART:20241016T073000Z
DTEND:20241016T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/63
DESCRIPTION:Title: Isotropic points in the Balmer spectrum of stable
motivic homotopy categories\nby Peng Du as part of Moscow-Beijing top
ology seminar\n\n\nAbstract\nI will discuss the tensor-triangulated geomet
ry of the stable motivic homotopy category SH(k) and a big family of the
so-called isotropic realisation functors\, parameterized by the choices
of a Morava K-theory and an extension of the base field k (of charact
eristic zero). By studying the target category of such an isotropic rea
lisation functor\, we are able to construct the so-called isotropic Mora
va points of the Balmer spectrum Spc(SH(k)^c) of the stable motivic h
omotopy category SH(k). This is based on joint work with Alexander Vishi
k.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Y. Vesnin
DTSTART:20241023T073000Z
DTEND:20241023T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/64
DESCRIPTION:Title: Polynomials of complete spatial graphs and Jones polyn
omials of related links\nby Andrey Y. Vesnin as part of Moscow-Beijing
topology seminar\n\n\nAbstract\nSpatial graphs are embeddings of graphs
in three-dimensional space. With each spatial graph one can relate consti
tuent knots formed by embeddings of cycles. The study of spatial graphs u
ses both combinatorial and topological methods.\nDenote by K4 a complete
graph with four vertices. We will discuss spatial K4-graphs and related
knots and links. We will present formular connecting normalized Yamada po
lynomial of a spatial K4-graph and Jones polynomials of a collection of k
nots and links related.\nThe talk is based on a joint work with Olga Oshma
rina\, see arXiv:2404:12264.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayato Imori
DTSTART:20241030T073000Z
DTEND:20241030T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/65
DESCRIPTION:Title: Instantons\, Khovanov homology\, and immersed cobordis
m maps\nby Hayato Imori as part of Moscow-Beijing topology seminar\n\n
\nAbstract\nThe functorial properties of homological knot invariants have
provided powerful tools for studying low-dimensional objects. Khovanov hom
ology and singular instanton Floer homology are such homological knot inva
riants. Kronheimer and Mrowka constructed a spectral sequence that links K
hovanov homology and a version of singular instanton Floer homology\, demo
nstrating that Khovanov homology can detect the unknot. In this talk\, we
will show that Kronheimer-Mrowka's spectral sequence relates cobordism map
s in Khovanov homology theory and instanton Floer theory. Furthermore\, ou
r construction includes induced maps for immersed cobordisms between knots
. This result also has topological applications related to knot concordanc
e and exotic phenomena of immersed surfaces in 4-manifolds. This talk is b
ased on joint work with Taketo Sano\, Kouki Sato\, and Masaki Taniguchi.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rama Mishra
DTSTART:20241120T073000Z
DTEND:20241120T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/66
DESCRIPTION:Title: Parameterizing Real rational knots by Gluing\nby R
ama Mishra as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn th
is talk we discuss that knots in real projective three space can be parame
trized by embedding given by homogeneous polynomials of same degree.\nSuch
knots are referred as real rational knots. We show that the problem of c
onstructing a real rational knot of a reasonably low degree can be reduced
to an algebraic problem involving the pure braid group: expressing an ass
ociated element of the pure braid group in terms of the standard generator
s of the pure braid group. If time permits we also predict the existence o
f a real rational knot in a degree that is expressed in terms of the edge
number of its polygonal representation.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fyodor Ivlev
DTSTART:20241106T073000Z
DTEND:20241106T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/67
DESCRIPTION:Title: The boundness of distance between two sets of fixed vo
lume inside the multidimensional right figures of unite volume.\nby Fy
odor Ivlev as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIf we
consider the diameter of unit multidimensional cube it tends to the infin
ity when the number of the dimensions of the cube tends to infinity. But w
hat would be if we consider the distance between to sets of the fixed (but
small) volumes instead of the distance between two point\, whose volumes
are equal to 0? The Theorem is proven that this distance is bounded by a c
onstant not depending of the dimensions of the cube\, only by the initial
volumes of the sets. The similar question about the sphere or other right
figures (instead of the cube) are also considered. There are asymptotic ap
proximations of the limits of the maximum possible distance between such s
ets are given. For some figures the case of convex sets is considered more
precise.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20241113T073000Z
DTEND:20241113T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/68
DESCRIPTION:Title: A personal journey along Alexander polynomials\nby
Bao Vuong as part of Moscow-Beijing topology seminar\n\n\nAbstract\nI wil
l talk about somewhat a memorial story of my study about Alexander polynom
ials\, what I have learned\, what I would want to understand. Along the wa
y I got some elementary results on Alexander polynomials of links in Poinc
are homology sphere\, a work in progress on Fox-Milnor condition for knot
concordance in Poincare homology sphere.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg N. German
DTSTART:20241127T073000Z
DTEND:20241127T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/69
DESCRIPTION:Title: Theorems of Dirichlet\, Vahlen\, and Hurwitz\nby O
leg N. German as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe
will discuss some very simple yet elegant results that\, in various ways\
, strengthen Dirichlet's theorem on the approximation of real numbers by r
ationals. Both arithmetic proofs and geometric ones will be considered\, i
ncluding those employing Klein polygons—a geometric interpretation of co
ntinued fractions.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miztani Euich
DTSTART:20241204T073000Z
DTEND:20241204T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/70
DESCRIPTION:Title: Time-independent Special Theory of Relativity\nby
Miztani Euich as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn
the process of Albert Einstein establishing the theory of special relativ
ity\, the principle of relativity is completely based on a geometrical des
cription. On the other hand\, the electro-magnetic theory is purely algebr
aic and complicated. Minkowski’s work extended it for 4-dimensional spac
e-time which is purely algebraic as well. \n\nHowever\, we can understand
Einstein's ideas much simpler and more phenomenally in section 1. Such a d
escription of special relativity will facilitate research in spintronics t
o consider the relativistic effect. Besides\, it leads to an unknown speci
al orthogonal group in real space\, not the indefinite orthogonal group SO
(1\,3) in section 2. Furthermore\, long-standing controversies of displace
ment current will be solved in section 3. In this talk we discuss the ‘c
omplete’ geometric special relativity and its new Lie group in real spac
e.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weibiao Wang
DTSTART:20241211T073000Z
DTEND:20241211T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/71
DESCRIPTION:Title: Embeddability of non-orientable closed surfaces in 3-m
anifolds\nby Weibiao Wang as part of Moscow-Beijing topology seminar\n
\n\nAbstract\nWe know that non-orientable closed surfaces can not be embed
ded in the 3-sphere. Naturally\, we ask for a given 3-manifold which non-o
rientable closed surfaces can be embedded in it. For any lens space\, or t
he product of any surface and the circle\, the answer is known\, mainly by
the work of Bredon and Wood\, as well as those of Jaco\, End\, Rannard\,
and so on. I will review their results\, and then discuss embeddability of
non-orientable closed surfaces in surface bundles over the circle. For th
e total space of any torus bundle over the circle\, we determine the gener
a of non-orientable closed surfaces that can be embedded in it. This is jo
int work with Xiaoming Du and Yimu Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengyi Zhou
DTSTART:20241218T073000Z
DTEND:20241218T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/72
DESCRIPTION:Title: Kahler compactification of C^n and Reeb dynamics\n
by Zhengyi Zhou as part of Moscow-Beijing topology seminar\n\n\nAbstract\n
We will present two results in complex geometry: (1) A Kahler compactifica
tion of C^n with a smooth divisor complement must be P^n\, which confirms
a conjecture of Brenton and Morrow(1978) under the Kahler assumption\; (2)
Any complete asymptotically conical Calabi-Yau metric on C^3 with a smoot
h link must be flat\, confirming a modified version of Tian’s conjecture
regarding the recognition of the flat metric among Calabi-Yau metrics in
dimension 3. Both proofs rely on relating the minimal discrepancy number o
f a Fano cone singularity to its Reeb dynamics of the conic contact form.
This is a joint work with Chi Li.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gu Xing
DTSTART:20241225T073000Z
DTEND:20241225T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/73
DESCRIPTION:Title: Polynomial invariants and the cohomology of $BPU(p^m)$
\nby Gu Xing as part of Moscow-Beijing topology seminar\n\n\nAbstract\
nIn this talk\, invariant polynomials refer to polynomials over a prime fi
eld of positive characteristics that are invariant under some group action
s. We reveal several connections between invariant polynomials and the coh
omology of $BPU(p^m)$\, the classifying space of the projective unitary gr
oup $PU(p^m)$ where $p$ is an odd prime number.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Bludov
DTSTART:20250108T073000Z
DTEND:20250108T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/74
DESCRIPTION:Title: Balanced sets and homotopy invariants of covers\nb
y Mikhail Bludov as part of Moscow-Beijing topology seminar\n\n\nAbstract\
nIt is known that any covering of an $m$-dimensional sphere $S^m$ by $n \\
geq 2$ open (or closed) sets can be associated with a homotopy class of ma
ps from $S^m$ to $S^{n-2}$. We show that by considering certain $n$ points
in Euclidean space $\\mathbb{R}^d$\, this covering of the sphere $S^m$ ca
n also be associated with a homotopy class of maps from $S^m$ to $S^{d-1}$
. In the case $S^m = \\partial D^{m+1}$\, the resulting homotopy class\, w
hen nontrivial\, acts as an obstruction to certain extensions of the cover
ing to the entire disk $D^{m+1}$. Using this\, we derive the KKMS lemma\,
as well as its analogues and generalizations. We also show that modulo an
automorphism of order 2 on the homotopy group\, the homotopy class of the
covering does not depend on the choice of the set of points in $\\mathbb{R
}^d$\, provided that these sets are balancedly equivalent.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arina Filimonova
DTSTART:20250115T073000Z
DTEND:20250115T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/75
DESCRIPTION:Title: Morphisms generating Lyndon words\nby Arina Filimo
nova as part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe will dis
cuss the problem of characterizing morphisms that generate Lyndon words. T
his problem has been solved for the binary alphabet (Richomme\, Séébold
(2021))\, but for obvious reasons\, the obtained result can not be general
ized to alphabets of larger sizes. We will review the original result and
then discuss the possibility of reformulating it in a way that allows gene
ralization to larger alphabets. We will also discuss some potential approa
ches to achieving this generalization.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euich Miztani
DTSTART:20250122T073000Z
DTEND:20250122T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/76
DESCRIPTION:Title: Time-independent Special Theory of Relativity\nby
Euich Miztani as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn
the process of Albert Einstein establishing the theory of special relativ
ity\, the principle of relativity is completely based on a geometrical des
cription. On the other hand\, the electro-magnetic theory is purely algebr
aic and complicated. Minkowski’s work extended it for 4-dimensional spac
e-time which is purely algebraic as well. However\, we can understand Eins
tein's ideas much simpler and more phenomenally in section 1. Such a descr
iption of special relativity will facilitate research in spintronics to co
nsider the relativistic effect. Besides\, it leads to an unknown special
orthogonal group in real space\, not the indefinite orthogonal group SO(1\
,3) in section 2. Furthermore\, long-standing controversies of displacemen
t current will be solved in section 3. In this talk we discuss the ‘comp
lete’ geometric special relativity and its new Lie group and Lorentz cov
ariance in real space.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Sabak
DTSTART:20250129T073000Z
DTEND:20250129T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/77
DESCRIPTION:by Mohammed Sabak as part of Moscow-Beijing topology seminar\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov
DTSTART:20250312T073000Z
DTEND:20250312T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/78
DESCRIPTION:Title: String equation in the ring of differential operators
and the Dixmier conjecture for the first Weyl algebra\nby Alexander Zh
eglov as part of Moscow-Beijing topology seminar\n\n\nAbstract\nI will tal
k about the correspondence between the solutions of the string equation [P
\,Q]=1 in the ring of differential operators (and in particular\, in the f
irst Weyl algebra) and pairs of commuting ordinary differential operators
of rank one. The solutions of the string equation in the first Weyl algebr
a describe all its endomorphisms\, and thus it is possible to obtain condi
tions that single out endomorphisms that are not automorphisms (the Dixmie
r conjecture for the first Weyl algebra).\n The indicated correspondence i
s applied to the proof of the Dixmier conjecture\, the outline of which I
will try to present in the talk. The proof is also based on the theory of
normal forms for ordinary differential operators and the technique of Newt
on polygons for the first Weyl algebra.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyun Cheng (Beijing Normal University)
DTSTART:20250219T073000Z
DTEND:20250219T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/79
DESCRIPTION:Title: The construction of topological biquandles\nby Zhi
yun Cheng (Beijing Normal University) as part of Moscow-Beijing topology s
eminar\n\n\nAbstract\nA biquandle is a set equipped with two binary operat
ions\, which provides a set-theoretic solution of the Yang-Baxter equation
. A topological biquandle is a topological space with a compatible biquand
le structure. In this talk\, I will give a quick introduction to quandle t
heory and then explain how to construct some nontrivial examples of topolo
gical biquandles.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Melikhov
DTSTART:20250226T073000Z
DTEND:20250226T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/80
DESCRIPTION:Title: n-Quasi-isotopy and its applications\nby Sergey Me
likhov as part of Moscow-Beijing topology seminar\n\n\nAbstract\n0-Quasi-i
sotopy is just another name for link homotopy\, and the relations of k-qua
si-isotopy\, where k is a positive \ninteger\, are equivalence relations o
n PL (or smooth) links which are higher-order analogues of link homotopy\,
retaining \nsome key geometric properties of link homotopy. k-Quasi-isoto
py is closely related to type k invariants of links\, to Milnor's \n\\bar\
\mu-invariants with at most k+1 occurrences of each index and to the first
k+1 potentially nonzero coefficients of \nthe Conway polynomial\, as well
as to self C_{k+1}-equivalence\, (k+1)-cobordism of Cochran and Orr\, and
class k+1 \ngrope cobordism of Cochran\, Orr and Teichner. (The details\,
at least some of them\, will be reviewed in the talk.) In fact \nthe filt
ration extends to half-integer k\, and it turns out in particular that 0.5
-quasi-isotopy coincides with \\Delta-link homotopy \n(also known as self
C_2-equivalence).\n\nThe main applications of k-quasi-isotopy are to the r
elations of PL and topological isotopy. In particular\, if two PL links ar
e \ntopologically isotopic (=homotopic through embeddings)\, then they are
k-quasi-isotopic for all k\; and if they are \nk-quasi-isotopic for all k
\, then they are PL isotopic (=equivalent up insertion and deletion of loc
al knots) to a pair of PL links \nwhich are not separated by finite type i
nvariants. Thus D. Rolfsen's 1974 problem: "if two PL links are topologica
lly isotopic\, \nare they PL isotopic?" is solved affirmatively modulo the
well-known conjecture that PL links are separated by finite type \ninvari
ants. Among other applications of k-quasi-isotopy are partial results on a
nother 1974 problem of Rolfsen: "is every \n(topological) knot isotopic to
the unknot?" \n\nThe applications to isotopy are mostly new\, and were th
e main focus of a number of my recent talks\, including the ones at \nthe
Beijing-Moscow Mathematics Colloquium and the 10th Russia-China Conference
of Knot Theory and Related Topics. \nBy contrast\, the present talk will
mostly focus on k-quasi-isotopy itself\, for a fixed k\, and review result
s and open problems\nthat are mostly old (dating to 20-25 years ago) but s
eem to still interest some people.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Антон Белецкий
DTSTART:20250212T073000Z
DTEND:20250212T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/81
DESCRIPTION:Title: Итеративная теория малых сок
ращений И. Рипса и ее применение к пробл
еме Бернсайда\nby Антон Белецкий as part of M
oscow-Beijing topology seminar\n\n\nAbstract\nПроблема Бернс
айда широко известна как один из важнейш
их вопросов теории групп. Ключевой обла
стью\, позволившей достичь успехов в ее
решении\, стала так называемая теория ма
лых сокращений\, изучающая группы\, обра
зующие соотношения в которых слабо пере
секаются друг с другом (обощения этой т
еории используются в классической работ
е С. И. Адяна и П. С. Новикова\, а также в р
аботах А. Ю. Ольшанского)\nВ докладе будет
описано альтернативное построение гра
дуированной теории малых сокращений\, р
азработанное И. Рипсом. Мы постараемся г
еометрически исследовать свойства диаг
рамм Ван Кампена в группах\, где соотнош
ения схожих размеров слабо зацепляются
друг за друга\, и продемонстрируем прим
енимость этой теории для анализа групп Б
ернсайда. Желательно предварительное з
накомство с основными идеями теории мал
ых сокращений (вплоть до леммы Гриндлин
гера)\, однако необходимые определения и
мотивировки будут кратко даны в процесс
е доклада.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriy Bardakov
DTSTART:20250305T073000Z
DTEND:20250305T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/82
DESCRIPTION:Title: Multi-virtual braid groups and their representations\nby Valeriy Bardakov as part of Moscow-Beijing topology seminar\n\n\nAb
stract\nIn this talk we discuss multi-virtual braid groups and symmetric m
ulti-virtual braid groups which were introduced by Prof. Kauffman in 2024.
We de ne two normal subgroups of finite index subgroups of multi-virtua
l braid groups. Also\, we construct representations of multi-virtual braid
groups by automorphisms of some groups. At the end we give an answer on a
question of Prof. Kau man on non-triviality of 2-multi-virtual knots.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20250402T073000Z
DTEND:20250402T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/83
DESCRIPTION:Title: Are all 2-dimasional links in the 4-sphere slice?\
nby Eiji Ogasa as part of Moscow-Beijing topology seminar\n\n\nAbstract\nA
re all 2-dimasional links in the 4-sphere slice?\nIt is an outstanding ope
n question.\nWe introduce the speaker's partial solution and his related r
esults.\nWe talk about terminologies and history of this important questio
n.\nWe discuss other dimensional version of this question and the speaker'
s results.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Nawata
DTSTART:20250319T083000Z
DTEND:20250319T100000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/84
DESCRIPTION:Title: Skein algebras and DAHA\nby Satoshi Nawata as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nI will talk about the r
epresentation theory of double affine Hecke algebras in terms of brane qua
ntization on SL(2\,C)-character variety of a Riemann surface. In addition\
, I will explain the relation between DAHA and skein algebras\, and the re
lation to modular tensor categories.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satoshi Nawata
DTSTART:20250326T073000Z
DTEND:20250326T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/85
DESCRIPTION:Title: Skein algebras and DAHA\nby Satoshi Nawata as part
of Moscow-Beijing topology seminar\n\n\nAbstract\nI will talk about the r
epresentation theory of double affine Hecke algebras in terms of brane qua
ntization on SL(2\,C)-character variety of a Riemann surface. In addition\
, I will explain the relation between DAHA and skein algebras\, and the re
lation to modular tensor categories.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Chernov
DTSTART:20250409T073000Z
DTEND:20250409T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/86
DESCRIPTION:Title: Virtual Legendrian knots\, generalized Manturov projec
tion and corollaries\nby Vladimir Chernov as part of Moscow-Beijing to
pology seminar\n\n\nAbstract\nVirtual Legendrian knots were introduced by
Cahn and Levi and they are Legendrian knots in spherical cotangent bundles
of closed surfaces up to isotopy\, stabilization and destabilization of a
surface away from the front projection of the knot. The talk is based on
joint results with Sadykov. We briefly review Kuperberg type theorem for v
irtual Legendrian knots and their applications to the study of causality i
n Borde Sorkin spacetimes. We construct the generalization of Manturov pro
jection to such knots and apply this to the study of canonical genus and k
-arc crossing number for such knots.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanghzhou Liu
DTSTART:20250416T073000Z
DTEND:20250416T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/87
DESCRIPTION:Title: On the Burau & Lawrence-Krammer-Bigelow's representati
on\nby Yanghzhou Liu as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nThere are many interesting question:\n\n- How to map a braid to a
matrix?\n- What's the topology meaning of the representation?\n- Is the r
epresentations faithful?\n\nAs Prof. Manturov's the book said\, the basic
and the key lemma are very important for the 3rd point. So why are they tr
ue? This question allow us to explore the 2nd point. In fact\, it is very
beautiful construction.\n\nToday\, I will introduce some necessary details
about this topic: Burau & Lawrence-Krammer-Bigelow's representation.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miztani Euich
DTSTART:20250423T100000Z
DTEND:20250423T113000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/88
DESCRIPTION:Title: How Should We Interpret Space Dimension? — Trial for
a Mathematical Foundation in Higher Dimensional Physics\nby Miztani E
uich as part of Moscow-Beijing topology seminar\n\n\nAbstract\nIn modern p
hysics we could say that space dimension is derived from physical conditio
ns. Kaluza-Klein theory and D-brane are typical examples. However\, not on
ly by such conditions\, we should also think about space dimension with in
sights from known facts without any physical conditions. In this talk we r
ethink space dimensionality from scratch.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20250507T073000Z
DTEND:20250507T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/89
DESCRIPTION:Title: Transversals in iterated quasigroups and latin hypercu
bes of order 4\nby Anna Taranenko as part of Moscow-Beijing topology s
eminar\n\n\nAbstract\nA latin hypercube of order n is a multidimensional a
rray filled with n symbols such that each line contains all n symbols. A t
ransversal in latin hypercube is a diagonal that contains all distinct sym
bols. Given a binary quasigroup G of order n\, let the d-iterated quasigro
up G[d] be the (d+1)-dimensional latin hypercube equal to the Cayley table
of G composed with itself d times. In this talk\, we characterize latin h
ypercubes of order 4 that do not have transversals and describe a method f
or counting transversals in iterated quasigroups.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250430T073000Z
DTEND:20250430T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/90
DESCRIPTION:Title: Group $G_{n}^{3}$ with oriented triple points and brai
d invariant\nby Seongjeong Kim as part of Moscow-Beijing topology semi
nar\n\n\nAbstract\nIn 2015 the group $G_{n}^{3}$ is defined by V.O. Mantur
ov. By V.O. Manturov and I.M. Nikonov\, it is shown that there exists a we
ll-defined map from braid group to $G_{n}^{3}$ taking triple points.\nIn t
his talk\, we talk about modifications of group $G_{n}^{3}$ by determining
order of triple points on a line. We construct an invariant for pure brai
ds by using the modified $G_{n}^{3}$ and provide an example\, which could
not be distinguished with trivial braids by using $G_{n}^{3}$. In the end
of talk\, we discuss on further research.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART:20250514T073000Z
DTEND:20250514T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/91
DESCRIPTION:Title: Braiding and Folding Branched Covers of the 3-sphere.<
/a>\nby Scott Carter as part of Moscow-Beijing topology seminar\n\n\nAbstr
act\nGiven a knot or a link in the 3-dimensional sphere\, we consider bran
ched covers of the 3-sphere that are branched over the knot. The branched
covers are manufactured from the unbranched irregular covers of the knot c
omplement which are associated to homomorphisms of the fundamental group.
The branched covers can often be mapped into a tropical region of the 4-di
mensional sphere in such a way that the projection onto an equatorial 3-sp
here induces the branched cover. We will present several examples of such
folding and indicate how they can be constructed in general.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou LIU
DTSTART:20250521T073000Z
DTEND:20250521T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/92
DESCRIPTION:Title: From Knot Groups to Alexander Polynomial: A Non-standa
rd Algorithm\nby Yangzhou LIU as part of Moscow-Beijing topology semin
ar\n\n\nAbstract\nThis presentation is divided into two parts. First\, we
review the algebraic topology picture and significance of the Alexander po
lynomial\, from which we can obtain the "standard algorithm" for getting f
rom knot groups to the Alexander polynomial. In the second part\, I will s
hare a phenomenon discovered by Mr. Mingli Yuan\, which I personally call
the "non-standard algorithm" (compared to the above "standard algorithm").
After a large number of experimental verifications by Yuan\, it works for
many knots. Specifically\, if a knot group is generated by two generators
and has one relation\, i.e.\, \\( G = \\langle x\, y | R \\rangle \\)\, t
hen when \\( R \\) satisfies certain relations\, a very simple algorithm f
or obtaining the Alexander polynomial from it will be achieved: here\, \\(
x \\) represents the +1 operation\, and \\( y \\) represents the ×t oper
ation. Thus\, treating \\( R \\) as a string of instructions acting from r
ight to left\, \\( R(x) = x \\)\, and the expansion then gives the Alexand
er polynomial.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Завесов Александр Львович
DTSTART:20250528T073000Z
DTEND:20250528T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/93
DESCRIPTION:Title: Теория соседства\nby Завесов
Александр Львович as part of Moscow-Beijing topology semi
nar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kensuke Arakawa
DTSTART:20250611T073000Z
DTEND:20250611T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/94
DESCRIPTION:Title: Monoidal relative categories model monoidal (∞\,1)-c
ategories\nby Kensuke Arakawa as part of Moscow-Beijing topology semin
ar\n\n\nAbstract\nThis is a talk on higher category theory\, aimed at topo
logists in a broad sense. No prior experience with higher categories will
be assumed.\n\nHomotopical study of mathematical objects often starts by i
dentifying a subcategory of "weak equivalences" that behave like isomorphi
sms. In this spirit\, relative categories offer a minimalistic framework f
or homotopy theory: They are categories equipped with a designated subcate
gory of weak equivalences. A remarkable theorem of Barwick and Kan shows t
hat this simple structure in fact models (∞\,1)-categories. More precise
ly\, any relative category (C\,W) gives rise to an (∞\,1)-category C[W^{
-1}] by localizing at the weak equivalences. This process defines a functo
r\nRelCat[DK^{-1}]-->Cat_{(∞\,1)}\,\nwhere DK denotes the subcategory of
relative functors that induce equivalences of localizations. Barwick and
Kan showed that this functor is an equivalence.\n\nIn practice\, many rela
tive categories come equipped with a monoidal structure whose tensor produ
ct preserves weak equivalences in each variable. In such cases\, the local
ization inherits a monoidal structure. This raises a natural question: Do
monoidal relative categories model monoidal (∞\,1)-categories? The autho
r recently proved that the answer is yes\, borrowing techniques inspired b
y Segal's infinite loop space machine. In this talk\, we explain the ideas
behind the proof\, explore some applications\, and suggest possible gener
alizations.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fengling Li
DTSTART:20250604T073000Z
DTEND:20250604T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/95
DESCRIPTION:Title: A three-variable invariant of planar knotoids\nby
Fengling Li as part of Moscow-Beijing topology seminar\n\n\nAbstract\nAs a
generalization of the classical knots\, knotoids are equivalence classes
of immersions of the oriented unit interval in a surface. In recent years
\, a variety of invariants of spherical and planar knotoids have been cons
tructed as extensions of invariants of classical and virtual knots. In thi
s talk\, we introduce a three-variable transcendental invariant of planar
knotoids which is defined over an index function of a Gauss diagram. We de
scribe properties of this invariant and show that it is a Vassiliev invari
ant of order one. We provide lower bounds on the Gordian distance of homot
opic planar knotoids by using the transcendental invariant. This is joint
work with Wandi Feng and Andrei Vesnin.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Ray
DTSTART:20250618T073000Z
DTEND:20250618T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/96
DESCRIPTION:Title: Constructing locally flat surfaces in 4-manifolds (par
t 1)\nby Arunima Ray as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nThere are two main approaches to building locally flat surfaces i
n 4-manifolds: direct methods applying Freedman-Quinn's disc embedding the
orem\, and indirect methods using surgery theory. (Notably the second meth
od also requires the disc embedding theorem\, but only indirectly.) In thi
s sequence of two lectures\, I will give an introduction to both methods.
In this first lecture I will give a direct\, constructive proof of a resul
t of Lee-Wilczynski which states that every primitive second homology clas
s in a closed\, simply connected 4-manifold is represented by a locally fl
at torus.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Ray
DTSTART:20250625T073000Z
DTEND:20250625T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/97
DESCRIPTION:Title: Constructing locally flat surfaces in 4-manifolds (par
t 2)\nby Arunima Ray as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nThere are two main approaches to building locally flat surfaces i
n 4-manifolds: direct methods applying Freedman-Quinn's disc embedding the
orem\, and indirect methods using surgery theory. (Notably the second meth
od also requires the disc embedding theorem\, but only indirectly.) In thi
s sequence of two lectures\, I will give an introduction to both methods.
In this second lecture I will give a surgery-theoretic proof of a result o
f Freedman-Quinn\, which states that every Alexander polynomial one knot i
s topologically slice.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frolov Aleksandr
DTSTART:20250709T073000Z
DTEND:20250709T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/98
DESCRIPTION:Title: Motivic Knots and the Abhyankar-Moh Conjecture\nby
Frolov Aleksandr as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nThe Abhyankar-Moh theorem in affine algebraic geometry states that any p
olynomial embedding i:\\mathbb{C}\\hookrightarrow\\mathbb{C}^3 can be rect
ified. This means there exists a polynomial automorphism f of \\mathbb{C}^
3 such that f\\circ i = t \\mapsto (t\, 0\, 0).\n\nThe Abhyankar-Moh conje
cture generalizes this idea: It proposes that any polynomial embedding \\m
athbb{C}^k\\hookrightarrow\\mathbb{C}^n can be rectified\, for all dimensi
ons k and n. While this is known to hold when n > 2k + 1\, the conjecture
remains open even for specific cases. For example\, it is unsolved for the
embedding \\mathbb{C}\\hookrightarrow\\mathbb{C}^3 : t \\mapsto (t^3-3t\,
t^4-4t^2\, t^5-10t).\n\nA promising approach to this conjecture uses tech
niques from geometric topology\, especially knot theory. Recent research e
xplores how Morel-Voevodsky’s motivic homotopy theory can bridge topolog
ical methods and algebraic geometry\, offering new strategies for such pro
blems.\n\nIn this talk\, I will overview the basics of modern algebraic ge
ometry and motivic homotopy theory. The goal is to introduce motivic knots
and their invariants. Familiarity with commutative algebra and category t
heory is assumed.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20250723T073000Z
DTEND:20250723T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/99
DESCRIPTION:by Eiji Ogasa as part of Moscow-Beijing topology seminar\n\nAb
stract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuya Sakasai
DTSTART:20250716T073000Z
DTEND:20250716T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/100
DESCRIPTION:Title: On the structure of groups defined by Kim and Manturo
v\nby Takuya Sakasai as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nWe consider a series of groups $\\Gamma_n^4$ defined by Kim and M
anturov. These groups have their background in Delaunay triangulations of
a plane and they are expected to have relationships to many geometric obje
cts. In this talk\, by a group theoretical argument\, we show that the gro
ups $\\Gamma_n^4$ are finite for all n $\\ge 6$ and in fact they are 2-ste
p nilpotent 2-groups.\nThis is a joint work with Carl-Fredrik Nyberg-Brodd
a\, Yuuki Tadokoro and Kokoro Tanaka (arXiv: 2506.05778\, 2506.08050).\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akio Kawauchi
DTSTART:20250730T073000Z
DTEND:20250730T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/101
DESCRIPTION:Title: A survey on smooth unknotting of a surface-knot in th
e 4-space\nby Akio Kawauchi as part of Moscow-Beijing topology seminar
\n\n\nAbstract\nIt is explained how a smooth surface-knot in 4-space with
infinite cyclic fundamental group is a trivial surface-knot (i.e.\, the bo
undary of a smoothly embedded handlebody) in the 4-space. It is also expla
ined how a smooth surface-link in 4-space with meridian-based free fundame
ntal group is a trivial surface-link (i.e.\, the boundary of smoothly embe
dded disjoint handlebodies) in the 4-space. For these proofs\, the concept
of an orthogonal 2-handle pair on a surface-link is introduced and the pr
operties are explained\, with the property of uniqueness being particularl
y essential.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianru Duan
DTSTART:20250813T073000Z
DTEND:20250813T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/102
DESCRIPTION:Title: The L^2 Alexander torsion for links and its leading c
oefficient\nby Jianru Duan as part of Moscow-Beijing topology seminar\
n\n\nAbstract\nThe L^2-Alexander torsion is an invariant associated to a 3
-manifold and an 1-cohomology class. For an oriented link\, this invariant
is a real function with many properties similar to the classical Alexande
r polynomial. In this talk\, I will first review the basics of L^2-theory
of 3-manifolds (e.g. L^2-betti numbers\, L^2-torsions)\, then discuss the
"leading coefficient" of the L^2-Alexander torsion and show its connection
with Gabai's sutured manifold theory and the guts theory recently develop
ed by Agol-Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arunima Ray
DTSTART:20250820T073000Z
DTEND:20250820T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/103
DESCRIPTION:Title: The double star construction\nby Arunima Ray as p
art of Moscow-Beijing topology seminar\n\n\nAbstract\nI will describe a ne
w strategy to construct a pair of closed\, smooth 4-manifolds\, that are h
omotopy equivalent but not homeomorphic\, inspired by the star constructio
n. I will specifically focus on the constructive step\, which consists of
a sequence of explicit geometric manoeuvres.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Pan
DTSTART:20250827T083000Z
DTEND:20250827T100000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/104
DESCRIPTION:Title: Augmentations and Exact Lagrangian surfaces\nby Y
u Pan as part of Moscow-Beijing topology seminar\n\n\nAbstract\nExact Lagr
angian surfaces are important objects in the derived Fukaya category. Augm
entations are objects of the augmentation category\, which is the contact
analog of the Fukaya category. In this talk\, we discuss various relations
between augmentations and exact Lagrangian surfaces. In particular\, we r
ealize augmentations\, which is an algebraic object\, fully geometrically
via exact Lagrangian surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannik Schuler
DTSTART:20250806T073000Z
DTEND:20250806T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/105
DESCRIPTION:Title: Refined Gromov-Witten invariants\nby Yannik Schul
er as part of Moscow-Beijing topology seminar\n\n\nAbstract\nGromov-Witten
theory is a framework for enumerating holomorphic curves in a Kähler man
ifold X. The case where X is Calabi-Yau of complex dimension three is part
icularly rich and features connections to seemingly unrelated areas in mat
hematics and mathematical physics\, for instance knot invariants. I will i
ntroduce a refinement of Gromov-Witten invariants of Calabi-Yau threefolds
as proposed in joint work with A. Brini. I will explain how our proposal
formalises certain ideas in mathematical physics and mention several sanit
y checks our proposal passes. I will discuss applications and relations be
tween our refinement and other developments in enumerative geometry. Speci
al emphasis will be on refined knot invariants where I will comment on cur
rent obstructions and possible gains.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Ogasa
DTSTART:20250917T073000Z
DTEND:20250917T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/106
DESCRIPTION:Title: An extension of Khovanov-Lipshitz-Sarkar homotopy typ
e\nby Eiji Ogasa as part of Moscow-Beijing topology seminar\n\n\nAbstr
act\nIt is an open question whether Khovanov-Lipshitz-Sarkar homotopy type
can be extend to all manifolds. Kauffman\, Nikonov\, and the speaker exte
nd it to thickened surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ueki Jun\, Hyuga Yoshizaki
DTSTART:20250924T073000Z
DTEND:20250924T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/107
DESCRIPTION:Title: The p-adic class numbers of number fields\, elliptic
curves\, knots\, and graphs\nby Ueki Jun\, Hyuga Yoshizaki as part of
Moscow-Beijing topology seminar\n\n\nAbstract\npart 1 -- graphs -- (30 mi
n) \n by Jun Ueki (Ochanomizu University) \n\npart 2 --- number fields\,
elliptic curves\, and knots -- (60 min) \n by Hyuga Yoshizaki (Tokyo Sc
ience University) \n\nAbstract. \nLet $p$ be a prime number. As initiall
y pointed out by Sinnott--Han--Kisilevsky and afterward re-discovered by u
s\, in a pro-$p$ extension of number fields or its various analogues\, the
class number p-adically converges. In a topological setting\, the $p$-adi
c limit value (say\, the $p$-adic class number) may be interpreted as Kion
ke's $p$-adic torsion. \nWe will give numerical observations on this pheno
menon and point out further interests\, especially in a view of Lang--Trot
ter conjecture. \n(This talk is partially based on joint works with Reo Ko
bayashi and Sohei Tateno.)\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Abrosimov
DTSTART:20250910T073000Z
DTEND:20250910T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/108
DESCRIPTION:Title: Volumes of non-Euclidean tetrahedra\nby Nikolay A
brosimov as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe tal
k will provide an overview of the latest results on finding exact formulas
for calculating the volumes of hyperbolic tetrahedra. The classical formu
la of G. Sforza [1] expresses the volume of a general hyperbolic tetrahedr
on in terms of dihedral angles. Its modern proof is proposed in [2]\, wher
e a version of the Sforza formula for the volume of a spherical tetrahedro
n is also given. A formula in terms of edge lengths was obtained in [3]. T
he known formulas for the volume of a general hyperbolic tetrahedron are c
omplicated and cannot always be applied to calculate the volumes of more c
omplex polyhedra. A natural question arises about finding simpler formulas
for sufficiently wide families of hyperbolic tetrahedra. \nIn the second
part of the talk\, we will consider hyperbolic tetrahedra of special types
: ideal\, biorthogonal\, trirectangular\, and their generalizations. The v
olume of an ideal and biorthogonal hyperbolic tetrahedron was known to N.I
. Lobachevsky. We will present new formulas for calculating the volume and
normalized volume of a hyperbolic trirectangular tetrahedron [4]\, as wel
l as its generalization for a 4-parameter family of tetrahedra with one ed
ge orthogonal to a face. The latter formulas can be used to calculate the
volumes of more complex polyhedra in Lobachevsky space.\nAt the end of the
talk\, we will present a new formula for calculating the volume of a sphe
rical trirectangular tetrahedron [5]. The list of Coxeter's spherical tetr
ahedra was constructed in [6]. Coxeter showed that there are 11 types of s
uch tetrahedra in S^3. We will show that exactly 5 of these types belong t
o the family of trirectangular tetrahedra. We will calculate their volumes
to verify our formula.\n\nReferences:\n[1] Sforza G.\, Spazi metrico-proi
ettivi. Ricerche di Estensionimetria Integrale. Ser. 1907. III\, VIII (App
endice). P.41–66.\n\n[2] Abrosimov N.V.\, Mednykh A.D.\, Volumes of poly
topes in constant curvature spaces. Fields Inst. Commun. 2014. V.70. P.1
–26. arXiv:1302.4919\n\n[3] Abrosimov N.\, Vuong B.\, Explicit volume fo
rmula for a hyperbolic tetrahedron in terms of edge lengths. Journal of Kn
ot Theory and Its Ramifications. 2021. V.30. No.10\, 2140007. arXiv:2107.0
3004\n\n[4] Abrosimov N.\, Stepanishchev S.\, The volume of a trirectangul
ar hyperbolic tetrahedron. Siberian Electronic Mathematicsl Reports. 2023.
V.20. No.1\, P.275–284.\n\n[5] Abrosimov N.\, Bayzakova B.\, The volume
of a spherical trirectangular tetrahedron. Siberian Electronic Mathematic
sl Reports. 2025. V.22. No.1\, P.892–904.\n\n[6] Coxeter H.S.M.\, Discre
te groups generated by reflections. Ann. Math. 1934. V.35. P.588–621.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20250903T073000Z
DTEND:20250903T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/109
DESCRIPTION:Title: Multidimensional matrices in algebraic hypergraph the
ory\nby Anna Taranenko as part of Moscow-Beijing topology seminar\n\n\
nAbstract\nThe main goal of the presented study is to develop methods for
working with multidimensional matrices that can be applied to problems of
existence and enumeration of various structures in hypergraphs. Many resul
ts in the search for substructures in graphs are based on certain correspo
ndences between graphs and matrices and the application of linear algebra
methods. Among the most important topics in the combinatorial matrix theor
y are the representation of graphs using adjacency and incidence matrices\
, the Konig-Hall theorem for systems of distinct representatives\, the per
manents of doubly stochastic matrices\, and Latin squares. We generalize t
hese directions to multidimensional matrices and hypergraphs and lay the f
oundations of the combinatorial theory of multidimensional matrices.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Tiskin
DTSTART:20251008T073000Z
DTEND:20251008T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/110
DESCRIPTION:Title: The surprising algebra of string comparison\nby A
lexander Tiskin as part of Moscow-Beijing topology seminar\n\n\nAbstract\n
There is a surprising close connection between three seemingly unrelated s
tructures:\n\n- the longest common subsequence of strings and its behavior
under string concatenation\;\n- a certain class of integer matrices (unit
-Monge matrices)\, considered as a monoid under tropical multiplication\;\
n- the Hecke monoid\, or "sticky braid" monoid\, which can be regarded as
the classical braid group where inversion is replaced by idempotence of th
e generators.\n\nThese structures\, despite their different nature\, are i
n fact isomorphic\, so they represent different views of the same underlyi
ng structure. We will describe an efficient multiplication algorithm in th
is structure and its applications to various string comparison and approxi
mate pattern matching problems.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shoma Sugimoto
DTSTART:20251001T073000Z
DTEND:20251001T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/111
DESCRIPTION:Title: An abelian categorification of $\\hat{Z}$-invariants<
/a>\nby Shoma Sugimoto as part of Moscow-Beijing topology seminar\n\n\nAbs
tract\nThe $\\hat{Z}$-invariant is a $q$-series valued quantum invariant f
or (negative definite plumbed) 3-manifolds introduced by Gukov--Pei--Putro
v--Vafa in 2017. It provides not only a $q$-expansion of the Witten--Reshe
tikhin--Turaev invariant\, but also rich examples of ``spoiled" modular fo
rms such as mock/false theta functions. The latter fact suggests the exist
ence of non-rational vertex operator algebras (log VOAs) with $\\hat{Z}$-i
nvariants as their $q$-characters. However\, the study of log VOAs is stil
l underdeveloped\, and no examples of such log VOAs have been found so far
except for the two easiest cases (3- or 4-leg star graphs).\nThis talk wi
ll outline the ``nested Feigin--Tipunin construction" introduced and devel
oped by the speaker to provide a unified construction/research methodology
of the above correspondence between log VOAs and (negative definite plumb
ed) 3-manifolds. It enables us to construct and study the abelian category
of modules over the hypothetical log VOAs via the recursive application o
f the purely Lie algebraic geometric representation theory of FT construct
ion. In particular\, the corresponding $\\hat{Z}$-invariants are reconstru
cted in the Grothendieck group via the recursive application of the Weyl-t
ype character formula. From a theoretical physics perspective\, the nested
FT construction can be viewed as the algebraic counterpart to the contrib
ution from 3d $\\mathcal{N}=2$ theory in the $\\hat{Z}$-invariants.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay
DTSTART:20251022T073000Z
DTEND:20251022T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/112
DESCRIPTION:Title: On a positivity property of a solution of discrete Pa
inlevé equations\nby Anton Dzhamay as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nWe consider a particular example of a discrete Pai
nlevé equation arising from a construction of quantum minimal surfaces by
Arnlind\, Hoppe and Kontsevich. Observing that this equation corresponds
to a very special choice of parameters (root variables) in the Space of In
itial Conditions for the differential Painlevé V equation\, we show that
some explicit special function solutions\, written in terms of modified Be
ssel functions\, for d-PV yield the unique positive solution for some init
ial value problem for the discrete Painlevé eqyuation needed for quantum
minimal surfaces. This is a joint work with Peter Clarkson\, Andy Hone\, a
nd Ben Mitchell.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20251015T073000Z
DTEND:20251015T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/113
DESCRIPTION:Title: On the Unfaithfulness of the Manturov-Nikonov Map
\nby Yangzhou Liu as part of Moscow-Beijing topology seminar\n\n\nAbstract
\nThe representation theory of braid groups has advanced significantly bey
ond that of classical knots\, with several foundational linear representat
ions established. These include the Burau representation (which is known t
o be unfaithful for Bn when n≥5)\, the Temperley–Lieb representation (
closely related to the Jones polynomial)\, and the Lawrence–Krammer–Bi
gelow representation (faithful for all n≥1). In 2022\, Professor Manturo
v and Professor Nikonov introduced a map from classical braids to virtual
braids\, extending the framework of braid group representations into the d
omain of virtual knot theory. This talk will demonstrate that the Manturov
-Nikonov map is unfaithful by constructing explicit counterexamples.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Kalinin
DTSTART:20251105T073000Z
DTEND:20251105T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/114
DESCRIPTION:Title: Tropical Weil Reciprocity\nby Nikita Kalinin as p
art of Moscow-Beijing topology seminar\n\n\nAbstract\nThe classical Weil r
eciprocity law is a fundamental result in the theory of algebraic curves\,
stating that for two meromorphic functions on a compact Riemann surface\,
the product of the values of one function at the divisors of the other is
equal to the reciprocal product. In this talk\, we explore a tropical ana
logue of this law.\n \n We will begin by introducing tropical curves and
tropical meromorphic functions. We then state and prove the tropical Weil
reciprocity law\, which takes a strikingly simple linear form. This tropi
cal perspective not only provides a new\, combinatorial viewpoint but also
leads to an elegant proof of the original\, classical Weil reciprocity la
w. The proof strategy involves decomposing the Riemann surface into simple
pieces (cylinders) and observing how the relevant contributions cancel up
on gluing.\n \n Finally\, we will discuss how this framework allows for
the construction of a tropical Weil pairing on the group of divisors of de
gree zero\, drawing an analogy with electrical networks and suggesting a c
onnection to its classical counterpart. This is joint work with M. Magin.\
n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshio Saito
DTSTART:20251119T073000Z
DTEND:20251119T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/115
DESCRIPTION:Title: From Flow Spines to Virtual Knot Diagrams: A Risandle
Approach to 3-Manifold Invariants\nby Toshio Saito as part of Moscow-
Beijing topology seminar\n\n\nAbstract\nEvery oriented closed 3-manifold a
dmits a flow spine\, that is\, a spine in a “good” position with respe
ct to a given nonsingular flow. A flow spine can be represented by a virtu
al knot diagram\, where equivalence is defined through a family of local m
oves different from the classical Reidemeister moves.\nIn this talk\, we i
ntroduce a modified version of the quandle algebra\, originally useful in
knot theory\, to define a new notion of “coloring” for closed 3-manifo
lds. This coloring yields a topological invariant of 3-manifolds. Furtherm
ore\, I will explain how this invariant is related to the fundamental grou
p of the manifold. The correspondence between colorings and group represen
tations will be illustrated concretely using the Poincaré homology sphere
as an example. This work is a joint project with Ippei Ishii and Takuji N
akamura.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20251029T073000Z
DTEND:20251029T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/116
DESCRIPTION:Title: A characterization of virtual knots as knots in $S_{g
} \\times S^{1}$\nby Seongjeong Kim as part of Moscow-Beijing topology
seminar\n\n\nAbstract\nIn this talk we will show that virtual knots are e
mbedded in the set of knots in $S_{g} \\times S^{1}$. We will also provide
a sufficient condition for knots in $S_{g} \\times S^{1}$ to have virtual
knot diagrams.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Bazhenov (Sobolev Institute of Mathematics\, Novosibirsk\,
Russia)
DTSTART:20251203T073000Z
DTEND:20251203T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/117
DESCRIPTION:Title: On computability-theoretic aspects of Stone spaces\nby Nikolay Bazhenov (Sobolev Institute of Mathematics\, Novosibirsk\, R
ussia) as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe roots
of computable analysis go back to the seminal work of Turing (1936). One
of the main directions in contemporary computable analysis studies computa
bility aspects of Polish spaces. A computable Polish space is a Polish spa
ce equipped with a distinguished dense countable sequence of points such t
hat the distances between these points are uniformly computable.\nIn the t
alk\, we focus on Stone spaces. Recall that a Stone space is a compact and
totally disconnected Hausdorff space. The classical result of Stone estab
lished a duality between the category of Stone spaces and the category of
Boolean algebras. We give an overview of some recent results on the comput
ability-theoretic properties of separable Stone spaces. In particular\, we
discuss effective versions of the Stone duality.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaebaek Lee
DTSTART:20251112T073000Z
DTEND:20251112T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/118
DESCRIPTION:Title: The Ramsey Multiplicity Problem\nby Jaebaek Lee a
s part of Moscow-Beijing topology seminar\n\n\nAbstract\nA graph $H$ is sa
id to be \\emph{common} if the number of monochromatic copies of $H$ is as
ymptotically minimized by a random colouring. It is well known that the di
sjoint union of two common graphs may be uncommon\; e.g.\, $K_2$ and $K_3$
are common\, but their disjoint union is not. We investigate the commonal
ity of disjoint unions of multiple copies of $K_3$ and $K_2$. As a consequ
ence of our results\, we obtain the first example of a pair of uncommon gr
aphs whose disjoint union is common. Our approach is to reduce the problem
of showing that certain disconnected graphs are common to a constrained o
ptimization problem in which the constraints are derived from supersaturat
ion bounds related to Razborov's Triangle Density Theorem. We also improve
the bounds on the Ramsey multiplicity constant of a triangle with a penda
nt edge and the disjoint union of $K_3$ and $K_2$.\nFox and Wigderson rece
ntly identified a large family of graphs whose Ramsey multiplicity constan
ts are attained by sequences of ``Tur\\'an colourings\;'' i.e. colourings
in which one of the colour classes forms the edge set of a balanced comple
te multipartite graph. Each graph in their family comes from taking a conn
ected non-3-colourable graph with a critical edge and adding many pendant
edges. \nWe focus on finding smaller graphs whose Ramsey multiplicity cons
tants are achieved by Tur\\'an colourings. While Fox and Wigderson provid
e many examples\, their smallest constructions involve graphs with at leas
t $10^{66}$ vertices. In contrast\, we identify a graph on only $10$ verti
ces whose Ramsey multiplicity constant is achieved by Tur\\'an colourings.
To prove this\, we apply the method developed earlier and use a powerful
technique known as the flag algebra method\, assisted by semi-definite pro
gramming.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun Wang
DTSTART:20251210T073000Z
DTEND:20251210T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/119
DESCRIPTION:Title: The multiple points of maps from sphere to Euclidean
space\nby Jun Wang as part of Moscow-Beijing topology seminar\n\n\nAbs
tract\nIt is obtained some sufficient conditions to guarantee the existenc
e of multiple points of maps from $S^m$ to $\\mathbb{R}^d$. Our main tool
is the ideal-valued index of $G$-space defined by E. Fadell and S. Hussein
i. We obtain more detailed relative positional relationship of multiple
points. It is proved that for a continuous real value function $f: S^m\\
rightarrow \\mathbb{R}$ such that $f(-p)=-f(p)$\, if $m+1$ is a power of
$2$\, then there are $m+1$ points $p_1\, \\ldots\, p_{m+1}$ in $S^m$ su
ch that $f(p_1)=\\cdots=f(p_{m+1})$\, where $p_1\, \\ldots\, p_{m+1}$ are
linearly dependent and any $m$ points of $p_1\, \\ldots\, p_{m+1}$ are li
nearly independent. As a generalization of Hopf's theorem\, we also prove
that for any continuous map $f: S^m\\rightarrow \\mathbb{R}^d$\, if $m> d
$\, then there exists a pair of mutually orthogonal points having the sam
e image in addition to the antipodal points.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang
DTSTART:20251126T073000Z
DTEND:20251126T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/120
DESCRIPTION:Title: Skein lasagna modules and Rozansky-Willis homology\nby Melissa Zhang as part of Moscow-Beijing topology seminar\n\n\nAbstra
ct\nIn this talk I will describe joint work with Ian Sullivan\, where we u
se properties of categorified projectors to prove that the Khovanov skein
lasagna module of $S^2 \\times S^2$ is trivial. Along the way\, we will di
scover a relationship between the skein lasagna module of $S^2 \\times D^2
$ with a link $L$ in the boundary and the Rozansky-Willis homology of $L$
inside $S^2 \\times S^1$. This isomorphism is used in recent joint work wi
th Qiuyu Ren\, Ian Sullivan\, Paul Wedrich\, and Michael Willis\, where we
define a new version of $gl_2$ skein lasagna modules with 1-dimensional i
nputs.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Николай Ероховец
DTSTART:20251217T073000Z
DTEND:20251217T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/121
DESCRIPTION:Title: Гиперболические зацепления\,
отвечающие эйлеровым циклам на идеальн
ых прямоугольных гиперболических мног
огранниках\,\nby Николай Ероховец as part of
Moscow-Beijing topology seminar\n\n\nAbstract\nМы расскажем о
конструкции\, позволяющей по эйлерову ци
клу C без трансверсальных самопересечен
ий на трёхмерном идеальном прямоугольно
м гиперболическом многограннике P постр
оить зацепление со следующими свойствам
и: \n(1) число его компонент равно числу ид
еальных вершин\, \n(2) дополнение гомеомор
фно полному гиперболическому многообра
зию\, склеенному из 4-х копий многогранни
ка P и получается из него конструкцией А.
Ю.Веснина-А.Д.Медных\, отвечающей шахматн
ой раскраске. \n(3) многообразие\, которое
двулистно разветвлённо накрывает сферу
вдоль этого зацепления\, получается конс
трукцией А.Д.Медных для гамильтонова цик
ла на другом простом многограннике Q\, оп
ределяемым циклом C (зацепления\, получае
мые в этой конструкции были недавно подр
обно исследованы В.Горчаковым). \n\nМы пок
ажем\, что на каждом идеальном многогран
нике\, кроме антипризм\, существует по кр
айней мере 7 таких циклов\, а на антипризм
ах — по крайней мере два. При этом на каж
дой антипризме есть один выделенный цик
л\, для которого конструкция сводится к к
онструкции У.П.Тёрстона.\n\nКак следствие
мы покажем\, что для каждого гамильтонов
а цикла \nна трёхмерном компактном прямо
угольном гиперболическом многограннике
дополнение до зацепления из конструкци
и А.Д.Медных\, разбивается на 4 идеальных
гиперболических многогранника (при этом
двулистная накрывающая тоже имеет гипе
рболическую структуру).\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brett Parker
DTSTART:20260107T073000Z
DTEND:20260107T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/122
DESCRIPTION:Title: Tropical perspectives on Skein modules.\nby Brett
Parker as part of Moscow-Beijing topology seminar\n\n\nAbstract\nI will e
xplain the connection between tropical curves\, skein modules\, and holomo
rphic curves in log Calabi—Yau 3-folds. In particular\, I will explain a
quantum deformation of Mikhalkin’s tropical correspondence formula\, an
d how a quantum torus lie algebra arises when counting closed holomorphic
curves in some log Calabi—Yau 3-folds. Apart from some pesky factors of
i\, this quantum torus lie algebra agrees with the elliptic Hall algebra d
escribing the skein algebra of the thickened torus. In fact\, there is a
beautiful explicit connection using Ekholm and Shende’s `skeins on brane
s’ formalism for counting holomorphic curves with boundaries on Lagrangi
an branes. I will illustrate this through two simple examples\, and explai
n why those pesky factors of i make me think that the worldsheet skein mod
ule introduced by Ekholm\, Longhi\, and Nakamura needs a simple modificati
on to account for some non-local contributions to orientations. The secon
d half of this talk is work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajat Mishra
DTSTART:20251224T073000Z
DTEND:20251224T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/123
DESCRIPTION:Title: Jet Spaces\, Differential Characters\, and Manin Kern
els\nby Rajat Mishra as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nLet K be a field of characteristic zero with a derivation ∂ on
it (for example\, (C(t)\, ∂/∂t)) and G be a smooth commutative group s
cheme over it. In this talk\, we study the kernel of the differential char
acters K(G) of the jet space of G\, known as the Manin kernel of G. When G
is an abelian variety\, Buium showed—using the theory of universal exte
nsions—that the Manin kernel is a D-group scheme and a finite vectorial
extension of G. We extend this result to arbitrary smooth commutative grou
p schemes\, proving that the Manin kernel K(G) remains a finite vectorial
extension of G. Our approach relies entirely on a detailed understanding o
f the structure of jet spaces and also yields a classification of the modu
le of differential characters in terms of primitive characters\, viewed as
a K{∂}-module. This is joint work with Arnab Saha.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malik Maricar
DTSTART:20251231T073000Z
DTEND:20251231T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/124
DESCRIPTION:Title: Introduction to phenomenological physics theory\, der
iving the Bohr Volume forms\, current applications in academia and industr
y\; regarding medicine and engineering\nby Malik Maricar as part of Mo
scow-Beijing topology seminar\n\n\nAbstract\nMy goal for the talk is to de
fine the Bohr Manifold—from how it came about to deriving its volume for
ms—Euclidean and the other Leibnizian. Thus\, make connections to publis
hed literature results including de Sitter by conformal field (4\,5) theor
y due to Juan Maldacena and at least another Juven C. Wang mentioned. Brie
fly\, discuss progression to the YM-Mass Gap solution and other problems l
isted by the Clay Mathematics Institute. Highlight\, current research work
applying from Manturov\, Nikonov\, Vogan to engineering in medicine and a
mong others\, Strominger\, Hong Liu\, Harlow\, and Wen Xiao Gang to furthe
r physics understanding of our universe invariant of scale\, including mat
hematics made possible by Zhang Wei\, Yun Zhi Wei and many others. Since\,
this will be my first ever talk—it will be informational\, remembering
the conferences and giving thanks to so many speakers presenting their wor
ks over the years contributing to my own research—with the main goal of
deriving the Bohr Volume Forms and to introduce a promising framework for
mathematicians. For the talk\, slides will be provided and if available te
chnology permits\, instruction will be on chalkboard.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreani Petrou
DTSTART:20260121T073000Z
DTEND:20260121T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/125
DESCRIPTION:Title: HOMFLY-PT and Kauffman polynomials: for which knots
are they related?\nby Andreani Petrou as part of Moscow-Beijing topolo
gy seminar\n\n\nAbstract\nTorus knots are long known to satisfy a special
relation between their HOMFLY-PT and Kauffman polynomials\, which has a pe
culiar implication in the context of Topological Strings. In this talk\, I
will describe infinite families of hyperbolic knots and links that enjoy
the same property. These were found via a physics-inspired tool called the
Harer-Zagier (HZ) transform\, which is a version of the Laplace transfor
m that maps the HOMFLY-PT polynomial into a rational function. It is conje
ctured that whenever the latter is factorisable\, the HOMFLY-PT-Kauffman r
elation occurs. I will explain how some steps towards a proof of this conj
ecture can be made\, at least for 3-strand braids\, by expanding these two
-variable link polynomials in terms of characters.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andronick Arutyunov
DTSTART:20260128T073000Z
DTEND:20260128T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/126
DESCRIPTION:Title: А combinatorial approach to derivations in algebras.
\nby Andronick Arutyunov as part of Moscow-Beijing topology seminar\n\
n\nAbstract\nUsing the following construction\, derivations in the sense o
f Leibniz\, as well as Fox derivatives and some other operators in algebra
s\, can be studied. First\, a category (usually a groupoid) is constructed
\, and then the operators are identified with the characters of the catego
ry. These characters are already can be studied using algebraic and combin
atorial methods\, which leads to questions related to rough geometry.\n\nT
his approach\, which was presented in a series of papers by the author and
Professor Mishchenko\, will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia V. Maslova (N.N. Krasovskii Institute of Mathematics and M
echanics UB RAS\, Yekaterinburg\, Russia Ural Mathematical Center\, Yekate
rinburg\, Russia S.L. Sobolev Institute of Mathematics SB RAS\, Novosibirs
k\, Russia)
DTSTART:20260114T073000Z
DTEND:20260114T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/127
DESCRIPTION:Title: On Gruenberg-Kegel graphs and beyond\nby Natalia
V. Maslova (N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS\
, Yekaterinburg\, Russia Ural Mathematical Center\, Yekaterinburg\, Russia
S.L. Sobolev Institute of Mathematics SB RAS\, Novosibirsk\, Russia) as p
art of Moscow-Beijing topology seminar\n\n\nAbstract\nThe Gruenberg--Kegel
graph (or the prime graph) of a finite group $G$ is a simple graph whose
vertices are the prime divisors of $|G|$\, with primes $p$ and $q$ adjacen
t in this graph if and only if $pq$ is an element order of $G$. The concep
t of Gruenberg--Kegel graph proved to be very useful in finite group theor
y and in algebraic combinatorics as well as with connection to research of
some cohomological questions in integral group rings. In this talk\, we d
iscuss recent results on characterization of finite groups by Gruenberg-Ke
gel graph and by isomorphism type of Gruenberg-Kegel graph as well as comb
inatorial properties of Gruenberg--Kegel graphs.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Ekholm
DTSTART:20260211T073000Z
DTEND:20260211T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/128
DESCRIPTION:Title: Skein valued curve counting\nby Tobias Ekholm as
part of Moscow-Beijing topology seminar\n\n\nAbstract\nWe describe how cou
nting curves in a symplectic Calabi-Yau 3-fold with boundary in a Maslov z
ero Lagrangian give a deformation invariant curve count. We then survey ap
plications including a proof of the Ooguri-Vafa conjecture and various sk
ein recursion relations.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Butian Zhang
DTSTART:20260204T073000Z
DTEND:20260204T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/129
DESCRIPTION:Title: Combinatorial 1-cocycles in the space of long knots\nby Butian Zhang as part of Moscow-Beijing topology seminar\n\n\nAbstra
ct\nThe space of long knots (i.e.\, the smooth embeddings of ℝ into ℝ
³ that agree with the standard embedding of the x-axis outside the interv
al [-1\, 1]) has been studied from various perspectives. In this talk\, we
adopt a combinatorial approach to loops and 1-cocycles in this space. Usi
ng Gauss diagrams\, we construct two nontrivial linearly independent combi
natorial 1-cocycles of order 4 over ℤ and an additional one over ℤ/2
ℤ. We also calculate their values on several arcs and loops in the space
of long knots. Furthermore\, we will discuss the joint work with T. Fiedl
er on the quantum equations derived from a regular 1-cocycle based on the
HOMFLY-PT polynomial.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiquan Ren (School of Mathematics and Statistics\, Henan Universi
ty\, China)
DTSTART:20260225T073000Z
DTEND:20260225T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/130
DESCRIPTION:Title: Homological obstructions for regular embeddings of gr
aphs\nby Shiquan Ren (School of Mathematics and Statistics\, Henan Uni
versity\, China) as part of Moscow-Beijing topology seminar\n\n\nAbstract\
nIn this talk\, we develop the hypergraph obstruction for the existence of
k-regular embeddings concretely and give some homological obstructions fo
r the k-regular embeddings of graphs by\nusing the embedded homology of su
b-hypergraphs of the (k−1)-skeleton of the independence\ncomplexes. We r
egard regular embeddings of graphs equivalently as geometric realizations
of the independence complexes and consequently regard them equivalently as
simplicial\nembeddings of the independence complexes into the vectorial m
atroids. We prove that if\nthere exists a k-regular embedding of a graph\,
then there is an induced homomorphism from\nthe embedded homology of the
sub-hyper(di)graphs of the (k − 1)-skeleton of the (directed)\nindepende
nce complexes to the homology of (directed) matroids. Moreover\, if there
exists\ncertain triple of graphs where each graph has a k-regular embeddin
g\, then there are induced commutative diagrams of certain Mayer-Vietoris
sequences of the embedded homology\nof hyper(di)graphs\, the homology of (
directed) independence complexes and the homology\nof matroids. Furthermor
e\, if there exists certain couple of graphs where each graph has\na k-reg
ular embedding\, then there are induced commutative diagrams of certain Ku
nneth\ntype short exact sequences of the embedded homology of hyper(di)gra
phs\, the homology of\n(directed) independence complexes and the homology
of matroids.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feidler Thomas
DTSTART:20260218T073000Z
DTEND:20260218T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/131
DESCRIPTION:Title: Polynomial 1-cocycles for closed braids and tangle eq
uations for knots\nby Feidler Thomas as part of Moscow-Beijing topolog
y seminar\n\n\nAbstract\nWe construct a combinatorial 1-cocycle for closed
braids. When applied to the full rotation of the solid torus around its c
ore it gives a Laurent polynomial which can sometimes detect the non-inver
tibility of the closed braid (what quantum invariants fail to do). In the
case of knots in 3-space we use another type of 1-cocycles to introduce th
e tangle equations. If they have no solution\, then the knots are not isot
opic. On the other hand\, each solution gives quantitative information abo
ut any isotopy which relates the two knots.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaiane Panina
DTSTART:20260401T073000Z
DTEND:20260401T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/132
DESCRIPTION:Title: A new proof of the Milnor – Wood theorem\, and beyo
nd\nby Gaiane Panina as part of Moscow-Beijing topology seminar\n\n\nA
bstract\nThe Milnor--Wood inequality states that if a (topological) orient
ed circle bundle over an orientable surface of genus $g$\nhas a smooth tra
nsverse foliation\, then the Euler class of the bundle satisfies $|E|\\leq
2g-2$.\nWe give a new proof of the inequality based on a (previously prov
en by the authors) local formula which computes \n$E$\n from the singulari
ties of a quasisection and present some more applications of this approach
.\n(Based on joint works with Ilya Alekseev\, Ivan Nasonov\, Timur Shamaz
ov and Maksim Turevskii)\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George B. Shabat
DTSTART:20260304T073000Z
DTEND:20260304T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/133
DESCRIPTION:Title: Introduction to dessins d'enfants Theory\nby Geor
ge B. Shabat as part of Moscow-Beijing topology seminar\n\n\nAbstract\nThe
theory of dessins d'enfants was created by Alexander Grothendieck from 19
72 to 1984. After a short historical overview I plan to talk about this th
eory in terms of the three-language vocabluary\, relating two-dimension to
pology\, group theory and algebraic geometry. The simplest examples will b
e provided.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem
DTSTART:20260318T073000Z
DTEND:20260318T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/134
DESCRIPTION:Title: Parity in Tensor Categories: From Hexagon Counting to
Virtual Knots\nby Semih Ozlem as part of Moscow-Beijing topology semi
nar\n\n\nAbstract\nTensor categories come equipped with associativity cons
traints\nϕ:(X⊗Y)⊗Z≅X⊗(Y⊗Z)\nand commutativity constraints\nΨ:X
⊗Y≅Y⊗X\,\nwhich must satisfy compatibility conditions encoded in hex
agon diagrams. For fixed objects X\,Y\,Z\, the full diagram of all tensor
products contains 20 distinct hexagons. A careful counting reveals 8 hexag
ons that obey an alternation rule (edges alternate between associativity a
nd commutativity) and 12 that do not. Under the natural S_3 action permuti
ng X\,Y\,Z\, these hexagons fall into orbits whose sizes (6 and 2 for alte
rnating hexagons) point to a mod 2 structure.\n \nWe show that this mod 2
structure can be interpreted as a parity grading on commutativity isomorph
isms\, satisfying a cocycle condition\np(X\,Y)+p(X⊗Y\,Z)≡p(Y\,Z)+p(X\,
Y⊗Z)mod2.\nThis parity function defines a parity projection functor Π:C
→C_virtual that sends even-parity commutativity isomorphisms to identiti
es while preserving odd-parity ones.\n \nThis functor provides a categoric
al realization of Manturov's map from the classical world to the virtual w
orld in knot theory. When applied to the braided tensor category of virtua
l tangles\, the construction recovers the parity bracket invariant. The tw
o orbits of alternating hexagons correspond to the two cohomology classes
in H2(S3\,Z2)≅Z2\, revealing a deep connection between tensor categories
\, knot parity\, and group cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangui Zhao
DTSTART:20260311T073000Z
DTEND:20260311T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/135
DESCRIPTION:Title: Growth of associated monomial algebras and Manturov g
roups\nby Xiangui Zhao as part of Moscow-Beijing topology seminar\n\n\
nAbstract\nIt is well-known that an associative algebra shares the same gr
owth and Gelfand-Kirillov dimension (GK-dimension) as its associated monom
ial algebra with respect to a degree-lexicographic order. In this talk\, w
e discuss the relationship between the GK-dimension of an associative alge
bra and that of its associated monomial algebra with respect to a monomial
order. As an application\, we study the growth of Manturov groups\, which
were introduced by V. Manturov in 2015.\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Shabat
DTSTART:20260325T073000Z
DTEND:20260325T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/136
DESCRIPTION:Title: Introduction to dessins d'enfants(continued)\nby
George Shabat as part of Moscow-Beijing topology seminar\n\n\nAbstract\nTh
e 3-language dictionary will be presented\, relating certain objects in\
n1) Bi-dimensional topology\;\n2) Group theory\;\n3) Arithmetic geometry.\
n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kursat Sozer
DTSTART:20260408T073000Z
DTEND:20260408T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/137
DESCRIPTION:by Kursat Sozer as part of Moscow-Beijing topology seminar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov
DTSTART:20260429T073000Z
DTEND:20260429T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/138
DESCRIPTION:by Alexander Zheglov as part of Moscow-Beijing topology semina
r\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Shabat
DTSTART:20260415T073000Z
DTEND:20260415T090000Z
DTSTAMP:20260404T111443Z
UID:Mos-Bei-top-seminar/139
DESCRIPTION:by George Shabat as part of Moscow-Beijing topology seminar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Mos-Bei-top-seminar/139/
END:VEVENT
END:VCALENDAR