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BEGIN:VEVENT
SUMMARY:Marcelo VIANA (IMPA - Rio de Janeiro)
DTSTART:20200527T130000Z
DTEND:20200527T140000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/1/">Lyapunov exponents</a>\nby Marcelo VIANA (IMPA - R
 io de Janeiro) as part of Colloquium del dipartimento di Matematica - Roma
  "Tor Vergata"\n\n\nAbstract\nThe concept of Lyapunov exponent goes back t
 o Lyapunov's 1892 thesis on the stability of differential equations\, and 
 has numerous applications in various branches of mathematics and science.\
 n\nStarting from the 1960s\, it found its proper mathematical framework in
  ergodic theory\, where it has had a prominent role ever since. In this co
 lloquium lecture I will review a few recent developments\, especially abou
 t the way Lyapunov exponents depend on the underlying dynamical system.\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Ghil (ENS and PSL University\, Paris\, and UCLA\, Los Ange
 les)
DTSTART:20200701T130000Z
DTEND:20200701T140000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/2/">Nonautonomous and random dynamical systems in the
  climate sciences</a>\nby Michael Ghil (ENS and PSL University\, Paris\, a
 nd UCLA\, Los Angeles) as part of Colloquium del dipartimento di Matematic
 a - Roma "Tor Vergata"\n\n\nAbstract\nH. Poincaré already raised doubts a
 bout the predictability of weather due to the divergence of orbits of dyna
 mical systems associated more recently with chaos. Progress in the theory 
 of nonlinear\, deterministic dynamical systems (DDS theory)\, on the one h
 and\, and the highly ingenious work of E.N. Lorenz\, on the other\, justif
 ied Poincaré’s early doubts. The theory of autonomous DDSs\, with time-
 independent forcing and coefficients\, provided a solid mathematical basis
  for much of the work on weather predictability over several decades.\nMor
 e recently\, an interesting and highly stimulating convergence occurred be
 tween studies of climate predictability\, on the one hand\, and the develo
 pment of the theory of nonautonomous and random dynamical systems (NDS and
  RDS)\, on the other. The diurnal and the seasonal cycle of insolation pla
 yed a somewhat limited role in weather predictability for 10–15 days\, b
 ut it became impossible to ignore the role of the seasonal cycle and of an
 thropogenic effects in climate predictability for years to decades.\nAt th
 e same time\, the theory of purely deterministic\, skew product flows\, as
  well as that of RDSs\, incorporated time-dependent forcing and coefficien
 ts and took huge mathematical strides\, including the rigorous formulation
  and application of pullback attractors. A parallel development in the phy
 sical literature formulated and applied in a more intuitive fashion the cl
 osely related concept of snapshot attractors.\nThese mathematical and phys
 ical advances were seized upon by several groups of researchers interested
  in climate modeling and predictability. In this talk\, I will try to pres
 ent some of the mathematical background\, as well as some of the applicati
 ons to the climate sciences. These will include\, as time permits: (i) the
  use of pullback and snapshot attractors for the proper understanding of t
 he effects of time-dependent forcing\, both deterministic and stochastic\,
  natural as well as anthropogenic\, upon intrinsic climate variability\; (
 ii) the use of Wasserstein distance between time-dependent invariant measu
 res to estimate these effects\; (iii) the topological aspects of nonautono
 mous effects upon the intrinsic variability\; and (iv) a “grand unificat
 ion” between the nonlinear\, deterministic and autonomous point of view 
 espoused by E.N. Lorenz and the linear\, stochastically driven one of K. H
 asselmann.\nThis talk reflects joint work with G. Charó\, M.D. Chekroun\,
  R. Durand\, A. DiGarbo\, Y. Feliks\, S. Galatolo\, F.-F. Jin\, D. Kondras
 hov\, V. Lucarini\, L. Marangio\, J.D. Neelin\, S. Pierini\, D. Sciamarell
 a\, E. Simonnet\, Y. Sato\, J. Sedro\, L. Sushama\, and I. Zaliapin.\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Catanese (University of Bayreuth)
DTSTART:20201105T133000Z
DTEND:20201105T143000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/3/">Nodal surfaces\, Coding theory\, and cubic discrim
 inants</a>\nby Fabrizio Catanese (University of Bayreuth) as part of Collo
 quium del dipartimento di Matematica - Roma "Tor Vergata"\n\n\nAbstract\nN
 odal surfaces in 3-space are those surfaces whose singularities have nonde
 generate Hessian. \nBasic numerical invariants are the degree d of a polyn
 omial defining such a surface Y\, and  the number \\nu of singular points.
  \nIf you fix those integers (d\,\\nu) these surfaces  are parametrized by
  the so-called Nodal Severi varieties F(d\, \\nu).  \n\nThe first basic qu
 estions are: \n\n1) for which pairs is F(d\, \\nu) nonempty ? \n2) When is
  it irreducible ?\n\nThe answer to 1) is known for d <= 6\, also the maxim
 al number of nodes \\mu (d)  that a nodal surface in 3-space of degree d c
 an have is known\nonly  for d <= 6.\n\nMaximizing nodal surfaces (those wi
 th \\mu(d) nodes) are: the Cayley cubic\, the Kummer surfaces\, the Toglia
 tti quintics\, the Barth sextic.\n\nAn important chapter in Coding theory 
 is the theory of binary linear codes\, vector subspaces of a vector space 
  (Z/2)^n.\n\nI will recall basic notions and methods of coding theory (e.g
 . the McWilliams identities) and describe some  codes related to quadratic
  forms. \n\nNodal surfaces are related to coding theory via the first homo
 logy of their smooth part: it  is a binary code K\, which was used  by Bea
 uville\nto show that\, for d=5 \, \\mu(d) = 31. Coding theory was crucial 
 in order to prove that \\mu(6) < = 65. \n\nOur main results concern the ca
 ses d = 4\,5\,6 (d=2\,3 being elementary). \n\nTHM 1. For d=4 the componen
 ts of  F(4\, \\nu) and their incidence correspondence are determined by th
 eir extended codes K’\,\nthese are all the shortenings of the first Reed
  Muller code.\n\nWe extend this result to nodal K3 surfaces of all degrees
 \, this sheds light on the case  d=5.\n\nTHM 2. For d=5  F(5\, \\nu) is ir
 reducible for \\nu = 31\, and the codes K occurring are classified\, up to
  a possible exception.\nFor \\nu = 29\,30\,31 these surfaces are discrimin
 ants of  of the projection of a cubic hypersurface in 5-space. \n\nTHM 3. 
 For d=6 and \\nu = 65  the codes K\, K’ are  uniquely determined\, and c
 an be described explicitly via\n the  Hall graph\, attached to the group \
 \SigmaL(2\, 25)\, and the gometry of the Barth sextic.\nEvery 65 nodal sex
 tic occurs as  discriminant of the projection of a cubic hypersurface in  
 6-space  with <=34  nodes.\n\n\nIrreducibility for d=6\, and 65 nodes\, is
  related to  the geometry of nodal cubic hypersurfaces in n-space\, and of
  the linear subspaces contained in them.\n\nOne may ask whether\, in the c
 ase of even dimension n\, the cubic hypersurface with maximal number of si
 ngularities is\nprojectively equivalent to the Segre cubic s_1=s_3=0.\n\nF
 or theorem 2  I benefited of the  cooperation of Sandro Verra\, for theore
 m 3 of Yonghwa Cho\, Michael Kiermaier\,  Sascha Kurz\nand the Linux Clust
 er of the Universitaet Bayreuth\,  while \nDavide Frapporti and Stephen Co
 ughlan cooperated for the geometry of nodal cubic hypersurfaces.\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Okounkov (Columbia University)
DTSTART:20201203T150000Z
DTEND:20201203T160000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/4/">Lie theory without groups</a>\nby Andrei Okounkov 
 (Columbia University) as part of Colloquium del dipartimento di Matematica
  - Roma "Tor Vergata"\n\n\nAbstract\nLie theory\, which deals with smooth 
 groups of transformations\, is one of the cornerstones of mathematics and 
 has great importance for both theory and applications. It is also visibly 
 limited\, as the globe of Lie groups has been explored and inhabited. Howe
 ver\, in recent years\, some new geometric and algebraic structures have b
 een recognized as being as good as Lie groups in every respect\, including
  e.g. their contribution to the supply of special functions. My goal in th
 is talk will be to explain where these new avenues of Lie theory lead.\n\n
 Note: This colloquium is part of the activity of the MIUR Department of Ex
 cellence Project CUP E83C18000100006\n\nThe talk will be streamed via Micr
 osoft Teams. \n\nLink:\nhttps://teams.microsoft.com/l/meetup-join/19%3a2a9
 a822955b54ca39f77f84130804b56%40thread.tacv2/1606245840781?context=%7b%22T
 id%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%229bfb10
 cf-6b03-47dc-906c-d23eb368824c%22%7d\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toshiyuki Kobayashi (The University of Tokyo)
DTSTART:20210218T130000Z
DTEND:20210218T140000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/5/">A foundation of group-theoretic analysis on manifo
 lds</a>\nby Toshiyuki Kobayashi (The University of Tokyo) as part of Collo
 quium del dipartimento di Matematica - Roma "Tor Vergata"\n\n\nAbstract\nS
 ymmetry of geometry is inherited by symmetry of function spaces\, called 
 the regular representation. From this viewpoint\, the classical theory of
  expansions such as Fourier series or spherical harmonics may be interpr
 eted as "analysis and synthesis" of the regular representation.\n\n\nIn t
 his talk\, we address the following fundamental questions about the regul
 ar representation on manifolds X acted algebraically by reductive Lie gro
 ups G such as GL(n\,R).\n\nA.  Does the group G "control well"  the spac
 e of function on X?\nB.  What can we say about "spectrum" for $L^2(X)$? 
 \n\nWe highlight "multiplicity" for A and "temperdness" for B\, and explai
 n some geometric ideas of the solution.\n\n<b>N.B.</b>:  <i>this talk is
  part of the activity of the MIUR Excellence Department Project CUP E83C18
 000100006</i>.\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas J.R. Hughes (The University of Texas at Austin)
DTSTART:20210426T150000Z
DTEND:20210426T160000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/6/">Isogeometric Analysis: Origins\, Status\, Recent 
 Progress and Structure Preserving Methods</a>\nby Thomas J.R. Hughes (The 
 University of Texas at Austin) as part of Colloquium del dipartimento di M
 atematica - Roma "Tor Vergata"\n\n\nAbstract\nThe vision of Isogeometric A
 nalysis (IGA) was first presented in a paper published October 1\, 2005 [1
 ].  Since then it has become a focus of research within both the fields of
  Finite Element Analysis (FEA) and Computer Aided Geometric Design (CAGD) 
 and has become a mainstream analysis methodology and provided a new paradi
 gm for geometric design [2-4].  The key concept utilized in the technical 
 approach is the development of a new foundation for FEA\, based on rich ge
 ometric descriptions originating in CAGD\, more tightly integrating design
  and analysis.  Industrial applications and commercial software developmen
 ts have expanded recently.  In this presentation\, I will describe the ori
 gins of IGA\, its status\, recent progress\, areas of current activity\, a
 nd the development of isogeometric structure preserving methods.\n\n\n<b>K
 ey Words</b>: <i>Computational Mechanics\, Computer Aided Design\, Finite 
 Element Analysis\, Computer Aided Engineering</i>\n<br>\n\n\n<b>REFERENCES
 </b>\n<br>\n[1]  T.J.R. Hughes\, J.A. Cottrell and Y. Bazilevs\, Isogeomet
 ric Analysis: CAD\, Finite Elements\, NURBS\, Exact Geometry and Mesh Refi
 nement\, Computer Methods in Applied Mechanics and Engineering\, 194\, (20
 05) 4135-4195.\n<br>\n[2]  J.A. Cottrell\, T.J.R. Hughes and Y. Bazilevs\,
  Isogeometric Analysis: Toward Integration of CAD and FEA\, Wiley\, Chiche
 ster\, U.K.\, 2009.\n<br>\n[3]  Special Issue on Isogeometric Analysis\, (
 eds. T.J.R. Hughes\, J.T. Oden and M. Papadrakakis)\, Computer Methods in 
 Applied Mechanics and Engineering\, 284\, (1 February 2015)\, 1-1182.\n<br
 >\n[4]  Special Issue on Isogeometric Analysis: Progress and Challenges\, 
 (eds. T.J.R. Hughes\, J.T. Oden and M. Papadrakakis)\, Computer Methods in
  Applied Mechanics and Engineering\, 316\, (1 April 2017)\, 1-1270.<br>\n\
 n\n<b>NB</b>:<i>This talk is part of the activity of the MIUR Excellence D
 epartment Project MATH@TOV CUP E83C18000100006</i>\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Gigli (SISSA Trieste)
DTSTART:20211216T150000Z
DTEND:20211216T163000Z
DTSTAMP:20260404T111444Z
UID:ColloquiumDiDipartimento/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Collo
 quiumDiDipartimento/7/">Differentiating in a non-differentiable environmen
 t</a>\nby Nicola Gigli (SISSA Trieste) as part of Colloquium del dipartime
 nto di Matematica - Roma "Tor Vergata"\n\n\nAbstract\nWe all know what the
  differential of a smooth map from R to R is. By looking at coordinates a
 nd then at charts\, we also know what it is the differential of a smooth m
 ap between differentiable manifolds. With a little bit of work\, we can a
 lso define a (weak) differential for Sobolev/BV maps in this setting (but 
 the case of manifold-valued maps presents challenges already at this level
 ). In this talk I will discuss how it is possible to differentiate maps b
 etween spaces that have no underlying differentiable structure at all. The
  concepts of Sobolev/BV maps in this setting will also be discussed. <br>
 <br>\n   <small>\n   <b>NB</b>:<i>This talk is part of the activity of the
  MIUR Excellence Department Project MATH@TOV CUP E83C18000100006</i>\n   <
 /small>\n
LOCATION:https://stable.researchseminars.org/talk/ColloquiumDiDipartimento
 /7/
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