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BEGIN:VEVENT
SUMMARY:Aaron Manning (UNSW Sydney)
DTSTART:20250611T040000Z
DTEND:20250611T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/1/">Counting Matrices Over Finite Rank Multiplicative Groups</a>
 \nby Aaron Manning (UNSW Sydney) as part of UNSW Number Theory Seminar\n\n
 Lecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nThere have b
 een many recent works regarding arithmetic statistics questions related to
  matrices with entries from sets of number theoretic interest. This includ
 es\, in particular\, providing upper bounds on the number of matrices with
  a prescribed rank\, determinant\, or characteristic polynomial\, over suc
 h a set. Motivated by some recent work by Alon and Solymosi (2023)\, we co
 nsider matrices with entries from finitely generated subgroups of the grou
 p of units of a field of characteristic zero. Such sets require a consider
 ably different approach to many that have been studied previously. The pri
 mary tools we require follow from the Subspace Theorem of Schmidt (1972) o
 n the simultaneous approximation of algebraic numbers by rational numbers.
 \n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Trudgian (UNSW Canberra)
DTSTART:20250611T050000Z
DTEND:20250611T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/2/">A convex hull\, a boundary drawn<br> Envelops points from du
 sk till dawn</a>\nby Timothy Trudgian (UNSW Canberra) as part of UNSW Numb
 er Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nA
 bstract\nMany results in number theory rely on bounding exponential sums. 
 The title (written\, like so many student assignments\, by ChatGPT) mentio
 ns a convex hull. The more we know about this set of points\, the better o
 ur knowledge of exponential sums. Applications abound! I will mention thes
 e and an online database in which everyone can contribute\n\nhttps://githu
 b.com/teorth/expdb\n\nall of which is joint work with Terry Tao and Andrew
  Yang.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Breuer (University of Newcastle)
DTSTART:20250625T040000Z
DTEND:20250625T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/3/">Coefficients of modular polynomials</a>\nby Florian Breuer (
 University of Newcastle) as part of UNSW Number Theory Seminar\n\nLecture 
 held in Room 4082\, Lawrence East (H13).\n\nAbstract\nModular polynomials 
 encode isogenies between pairs of elliptic curves and have applications to
  cryptography. Famously\, these polynomials have very large coefficients. 
 In this talk I will outline some recent results on the sizes and divisibil
 ity properties of these coefficients. Time permitting\, I will also touch 
 on the analogous situation for Drinfeld modular polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryce Kerr (UNSW Canberra)
DTSTART:20250625T050000Z
DTEND:20250625T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/4/">Poissonian pair correlation for real sequences</a>\nby Bryce
  Kerr (UNSW Canberra) as part of UNSW Number Theory Seminar\n\nLecture hel
 d in Room 4082\, Lawrence East (H13).\n\nAbstract\nThe Poissonian pair cor
 relation is a local statistic that captures strong pseudo-randomness in de
 terministic sequences. In a forthcoming paper with Lianf\, we provide new 
 sufficient conditions under which a real sequence exhibits the metric Pois
 sonian property. This will be a continuation of Liang’s talk a few weeks
  ago.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Harm (UNSW Sydney)
DTSTART:20250709T050000Z
DTEND:20250709T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/5/">Tackling the $\\varepsilon$ for primes in short arithmetic p
 rogressions</a>\nby Michael Harm (UNSW Sydney) as part of UNSW Number Theo
 ry Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract
 \nGiven a zero-free region and an average zero-density estimate for all Di
 richlet $L$-functions modulo $q$\, we refine the error terms of the prime 
 number theorem in all and almost all short arithmetic progressions. If we 
 e.g. assume the Generalized Density Hypothesis\, then as $x\\rightarrow \\
 infty$ the prime number theorem holds for any arithmetic progression modul
 o $q\\leq \\log^\\ell x$  for any $\\ell>0$ and in the interval $(x\,x+\\s
 qrt{x}\\exp(\\log^{2/3+\\varepsilon} x)]$ for any $\\varepsilon>0$. This r
 efines the classic interval $(x\,x+x^{1/2+\\varepsilon}]$.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Iyer (UNSW Sydney)
DTSTART:20250709T040000Z
DTEND:20250709T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/6/">Gaps between quadratic forms</a>\nby Siddharth Iyer (UNSW Sy
 dney) as part of UNSW Number Theory Seminar\n\nLecture held in Room 4082\,
  Lawrence East (H13).\n\nAbstract\nLet $\\triangle$ denote the integers re
 presented by the quadratic form $x^2+xy+y^2$ and $\\square_{2}$ denote the
  numbers represented as a sum of two squares. For a non-zero integer $a$\,
  let $S(\\triangle\,\\square_{2}\,a)$ be the set of integers $n$ such that
  $n \\in \\triangle$\, and $n + a \\in \\square_{2}$. We conduct a census 
 of $S(\\triangle\,\\square_{2}\,a)$ in short intervals by showing that the
 re exists a constant $H_{a} > 0$ with\n$$\n\\# S(\\triangle\,\\square_{2}\
 ,a)\\cap [x\,x+H_{a}\\cdot x^{5/6}\\cdot \\log^{19}x] \\geq x^{5/6-\\varep
 silon}\n$$\nfor large $x$. To derive this result and its generalization\, 
 we utilize a theorem of Tolev (2012) on sums of two squares in arithmetic 
 progressions and analyse the behavior of a multiplicative function found i
 n Blomer\, Brüdern & Dietmann (2009). Our work extends a classical result
  of Estermann (1932) and builds upon work of Müller (1989).\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Badziahin (University of Sydney)
DTSTART:20250723T040000Z
DTEND:20250723T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/7/">Can we generate "RSA-safe" values of polynomials</a>\nby Dmi
 try Badziahin (University of Sydney) as part of UNSW Number Theory Seminar
 \n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nA crucia
 l part of various cryptosystems such as RSA is to generate composite numbe
 rs $n=pq$ that are almost impossible to factorise. Among other restriction
 s\, that means that n needs to be huge (e.g. 2048 bits) and $p$ and $q$ ne
 ed to be primes of a similar size. Such numbers are not difficult to gener
 ate. But what if\, on top of that\, we require n to be a value $P(m)$ of a
  given polynomial $P$ with integer coefficients at an integer point $m$? T
 hen the problem becomes much less trivial. In this talk I will discuss how
  one can randomly generate such triples $(p\,q\,m)$ for quadratic and cubi
 c polynomials $P$. We will also see that $p$ and $q$ can be generated in s
 uch a way that $p/q$ is close to any given positive real number.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shanta Laishram (Indian Statistical Institute\, New Delhi)
DTSTART:20250723T050000Z
DTEND:20250723T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/8/">On a class of Monogenic polynomials</a>\nby Shanta Laishram 
 (Indian Statistical Institute\, New Delhi) as part of UNSW Number Theory S
 eminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nLe
 t $f(x) \\in \\mathbb{Z}[x]$ be an irreducible polynomial of degree\n$n$ a
 nd $\\theta$ be a root of $f(x)$. Let $K=\\mathbb{Q}(\\theta)$ be\nthe num
 ber field and $\\mathbb{Z}_K$ be the ring of algebraic integers\nof $K$. W
 e say $f(x)$ is monogenic if $\\{1\, \\theta\, \\ldots\,\n\\theta^{n-1} \\
 }$ is a $\\mathbb{Z}$-basis of $\\mathbb{Z}_K$.\n\nIn this talk\, we consi
 der the family of polynomials $f(x)=x^{n-km}(x^k+a)^m+b \\in \\mathbb{Z}[x
 ]$\, $1\\leq km< n$. We provide a necessary and sufficient conditions for 
 $f(x)$ to be monogenic.  As an\napplication\, we get a class of monogenic 
 polynomials having non\nsquare-free discriminant and Galois group $S_n$\, 
 the symmetric group\non $n$ symbols. This is a joint work with A. Jakhar a
 nd P. Yadav.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis Combes (University of Sydney)
DTSTART:20250917T040000Z
DTEND:20250917T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/9/">Selmer groups for mod p Galois representations</a>\nby Lewis
  Combes (University of Sydney) as part of UNSW Number Theory Seminar\n\nLe
 cture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nSelmer groups 
 are an important construction in modern number theory\, with their ranks e
 xpected to encode arithmetic information associated to their underlying ob
 jects. This is most obvious in conjectures like that of Bloch-Kato\, relat
 ing an $L$-value to the rank of a Selmer group of a $p$-adic Galois repres
 entation. In recent years\, mod $p$ Galois representations have started to
  receive similar attention\, partly due to Scholze's proof that many torsi
 on classes have their own associated representations. In this talk we will
  cover some basics of Selmer groups\, how to compute them for mod $p$ Galo
 is representations\, and how to formulate and test interesting conjectures
  regarding their ranks.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Fish (University of Sydney)
DTSTART:20250917T050000Z
DTEND:20250917T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/10/">Ehrhart spectra of large subsets in $\\Z^n$</a>\nby Alexand
 er Fish (University of Sydney) as part of UNSW Number Theory Seminar\n\nLe
 cture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nThe Ehrhart sp
 ectrum of a set $E$ in $\\Z^n$\, defined as the set of all Ehrhart polynom
 ials of simplices with vertices in $E$\, generalizing the notion of volume
  spectrum. We show that for any $E$ in $\\Z^n$ with positive upper Banach 
 density\, there is some integer $k$ such that the Ehrhart spectrum of $k\\
 Z^n$ is contained in the Erhard spectrum of $E$. This is a joint work with
  Michael Bjorkludn and Rickard Cullman both from Chalmers.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Afifurrahman (UNSW Sydney)
DTSTART:20251001T050000Z
DTEND:20251001T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/11/">Counting multiplicatively dependent integer vectors on a hy
 perplane</a>\nby Muhammad Afifurrahman (UNSW Sydney) as part of UNSW Numbe
 r Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAb
 stract\nWe give several asymptotic formulas and bounds for the number of m
 ultiplicativly dependent integer vectors of bounded height that lies on a 
 hyperplane\, extending the work of Pappalardi\, Sha\, Shparlinski and Stew
 art. Joint work with Valentio Iverson and Gian Cordana Sanjaya  (Universit
 y of Waterloo).\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bittu Chahal (IIIT Delhi)
DTSTART:20251001T040000Z
DTEND:20251001T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/12/">Chebyshev's bias for irrational factor function</a>\nby Bit
 tu Chahal (IIIT Delhi) as part of UNSW Number Theory Seminar\n\nLecture he
 ld in Room 4082\, Lawrence East (H13).\n\nAbstract\nChebyshev's bias is th
 e phenomenon that the number of prime quadratic nonresidues of a given mod
 ulus predominate over the prime quadratic residues\, in other words\, prim
 es are biased toward quadratic nonresidues. We study this bias question in
  the context of the irrational factor function $I_k(n)$\, defined by $I_k(
 n)=\\prod_{i=1}^lp_i^{\\beta_i}$\, where $n=\\prod_{i=1}^lp_i^{\\alpha_i}$
  and \n$$\\beta_i=\n\\left\\{\\begin{array}{cc}\n   \\alpha_i\,  & \\textr
 m{if }  \\alpha_i < k\,\\\\ \n   \\frac{1}{\\alpha_i}\,   & \\textrm{if } 
 \\alpha_i\\geq k.\\end{array}\\right.$$\nIn particular\, we introduce the 
 irrational factor function in both number field and function field setting
 s\, derive asymptotic formulas for their average value\, and establish $\\
 Omega$-results for the error term in the asymptotic formulas. Furthermore\
 , we study the Chebyshev's bias phenomenon for number field and function f
 ield analogues of sum of the irrational factor function\, under assumption
 s on the real zeros of Hecke $L$-functions associated with Hecke character
 s in the number field case.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liangyi Zhao (UNSW Sydney)
DTSTART:20251015T030000Z
DTEND:20251015T040000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/13/">When the eggs are fried</a>\nby Liangyi Zhao (UNSW Sydney) 
 as part of UNSW Number Theory Seminar\n\nLecture held in Room 4082\, Lawre
 nce East (H13).\n\nAbstract\nGrey\, dear friends\, is all unproven theory.
   Thus I mar the immortal words of a very witty and most unjustly abused i
 mmortal.  At the most recent meeting of Number Theory Down Under\, it was 
 suggested that the work of Kerr-Shparlinski-Wu-Xi on Kloosterman sums migh
 t be applied to improve an asymptotic formula of Gao-Zhao for the twisted 
 fourth moment of Dirichlet $L$-functions to certain prime power moduli\, a
 s this latter result was presented.  Can this idea work?  We heeded Sancho
  Panza's counsel that "you'll see when the eggs are fried" and greened the
  untested theory.  More specifically\, taking the above recommendation\, a
 s well as doing other things\, we extended the aforesaid moment result to 
 general moduli and significantly improved the error term.  I shall report 
 on this recent work (arXiv:2509.24690)\, joint with P. Gao and X. Wu\, dur
 ing this talk.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Bellotti (UNSW Canberra)
DTSTART:20251015T040000Z
DTEND:20251015T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/14/">A New Zero-Density Estimate for the Riemann Zeta Function c
 lose to the $1$-line</a>\nby Chiara Bellotti (UNSW Canberra) as part of UN
 SW Number Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13
 ).\n\nAbstract\nIn this talk we present a new type of zero-density estimat
 e for the Riemann zeta function close to the one-line. In particular\, we 
 show that the number of zeros in this region remains bounded by an absolut
 e constant when approaching the left edge of the Korobov–Vinogradov zero
 -free region. As a consequence\, we obtain an essentially optimal refineme
 nt of a result due to Pintz concerning the error term in the prime number 
 theorem.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youming Qiao (University of Technology Sydney)
DTSTART:20251029T040000Z
DTEND:20251029T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/15/">A quantum algorithm for $2\\times 2\\times 2$ tensor isomor
 phism over $\\mathbb{Z}$</a>\nby Youming Qiao (University of Technology Sy
 dney) as part of UNSW Number Theory Seminar\n\nLecture held in Room 4082\,
  Lawrence East (H13).\n\nAbstract\nWe present a quantum polynomial-time al
 gorithm that decides whether two tensors in $\\mathbb{Z}^2\\otimes\\mathbb
 {Z}^2\\otimes\\mathbb{Z}^2$ are in the same orbit under the natural action
  of $\\mathrm{GL}(2\, \\mathbb{Z})\\times\\mathrm{GL}(2\, \\mathbb{Z})\\ti
 mes\\mathrm{GL}(2\, \\mathbb{Z})$. This algorithm is a natural consequence
  of the works of Gauss (on composition laws)\, Bhargava (on higher composi
 tion laws)\, and Hallgren (on quantum algorithms for the principal ideal p
 roblem). An intriguing question is the case of $\\mathbb{Z}^3\\otimes\\mat
 hbb{Z}^3\\otimes\\mathbb{Z}^3$.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Ward (University of York)
DTSTART:20251105T030000Z
DTEND:20251105T040000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/16/">Sets of Exact(er) approximation order</a>\nby Benjamin Ward
  (University of York) as part of UNSW Number Theory Seminar\n\nLecture hel
 d in Room 4082\, Lawrence East (H13).\n\nAbstract\nIn this talk\, which is
  joint work with Simon Baker (Loughborough\, UK)\, I will introduce a quan
 titative notion of exactness within Diophantine approximation. Given funct
 ions Ψ : (0\, ∞) → (0\, ∞) and ω : (0\, ∞) → (0\, 1)\, we stud
 y the set of points that are Ψ-well approximable but not Ψ(1 − ω)-wel
 l approximable\, denoted E(Ψ\,ω). This generalises the set of Ψ-exact a
 pproximation order as studied by Bugeaud (Math. Ann. 2003). We prove resul
 ts on the cardinality and Hausdorff dimension of E(Ψ\,ω). In particular\
 , for certain functions Ψ we find a critical threshold on ω whereby the 
 set E(Ψ\,ω) drops from positive Hausdorff dimension to empty when ω is 
 multiplied by a constant. The results discussed can be found in [2510.1845
 1] A quantitative framework for sets of exact approximation order by ratio
 nal numbers.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Subham Bhakta (UNSW Sydney)
DTSTART:20251105T040000Z
DTEND:20251105T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/17/">Character sums with division polynomials of elliptic curves
 </a>\nby Subham Bhakta (UNSW Sydney) as part of UNSW Number Theory Seminar
 \n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nIn this 
 talk\, I will take you on a journey through the character sums of division
  polynomials evaluated at rational points on elliptic curves over prime fi
 elds\; a topic that first caught my attention near the end of my PhD\, ins
 pired by a 2009 paper of I. E. Shparlinski and K. E. Stange. These charact
 er values exhibit an “almost multiplicative” behaviour. Motivated by C
 howla’s conjectures on correlations of multiplicative functions\, I will
  first present a recent joint work with I. E. Shparlinski (2025) on the co
 rrelations of these character sums under shifts. I will then discuss some 
 bounds for these sums when twisted by various multiplicative functions.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas-Stephan Elsenhans (University of Sydney and University of 
 Würzburg)
DTSTART:20251029T030000Z
DTEND:20251029T040000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/18/">Numerical verification of the Collatz Conjecture</a>\nby An
 dreas-Stephan Elsenhans (University of Sydney and University of Würzburg)
  as part of UNSW Number Theory Seminar\n\nLecture held in Room 4082\, Lawr
 ence East (H13).\n\nAbstract\nThe Collatz conjecture (also known as the 3n
 +1 problem) is one of the most\npopular open problems in number theory. In
  this talk I will give an introduction to \na theoretical analysis of the 
 problem and explain which strategies are used for\na numerical verificatio
 n.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse J&auml&aumlsaari (University of Turku)
DTSTART:20260318T030000Z
DTEND:20260318T040000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/19/">On the real zeros of half-integral weight Hecke cusp forms<
 /a>\nby Jesse J&auml&aumlsaari (University of Turku) as part of UNSW Numbe
 r Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAb
 stract\nIn this talk I will discuss recent work concerning the distributio
 n of zeros of half-integral weight Hecke cusp forms of large weight on the
  surface $\\Gamma_0(4)\\backslash \\mathbb{H}$. In particular\, I will foc
 us on the so-called real zeros\, that is zeros on certain geodesic segment
 s on which the cusp form takes real values\, and give lower bounds for the
  number of these zeros.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Trudgian (UNSW Canberra)
DTSTART:20260318T040000Z
DTEND:20260318T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/20/">I&apos\;ve got Euclid&apos\;s\, I&apos\;ve got Al Gore\, I&
 apos\;ve got Rhythm\, who could ask for anything more?</a>\nby Timothy Tru
 dgian (UNSW Canberra) as part of UNSW Number Theory Seminar\n\nLecture hel
 d in Room 4082\, Lawrence East (H13).\n\nAbstract\nInspired by Gershwin\, 
 the title refers to the oldest (?) mathematical algorithm: the Euclid&apos
 \;s algorithm for division. This allows us to divide two numbers\, keep tr
 ack of remainders\, rinse &apos\;n&apos\; repeat\, and recover GCDs. I wil
 l discuss other algebraic settings: some rings are known to be Euclidean (
 meaning they have this algorithm)\, some are known not to be\; many are un
 known. I will end with a summary of <a href="https://arxiv.org/abs/2507.05
 862">recent work done</a> by Bagger\, Booker\, Kerr\, McGown\, Starichkova
 \, and me that resolves completely the case of cyclic cubic fields.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K&eacute\;va Djamba&eacute\; (University of French Polynesia)
DTSTART:20260415T040000Z
DTEND:20260415T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/21/">Explicit constructions of Galois Groups</a>\nby K&eacute\;v
 a Djamba&eacute\; (University of French Polynesia) as part of UNSW Number 
 Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbst
 ract\nIn this talk\, I will introduce the concepts and questions arising i
 n the explicit description of Galois groups over finite fields\, and prese
 nt a geometric construction based on isogeny cycles that allows for an exp
 licit computation of Galois automorphisms. This is based on the preprint a
 rXiv:2603.19428 (https://arxiv.org/abs/2603.19428).\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandler Corrigan (UNSW Sdyney)
DTSTART:20260429T040000Z
DTEND:20260429T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/23
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/23/">Transformation formulæ for exponential sums twisted by Hec
 ke eigenvalues</a>\nby Chandler Corrigan (UNSW Sdyney) as part of UNSW Num
 ber Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\n
 Abstract\nEstimates for exponential sums twisted by a fixed arithmetic fun
 ction play a central rôle in analytic number theory.  In particular\, suc
 h estimates can be used to study certain properties of the object associat
 ed to the chosen arithmetic function.  In this talk\, we discuss an analog
  of the van der Corput B-process in the case of Hecke eigenvalues for cong
 ruence subgroups.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad  Afifurrahman (UNSW Sdyney)
DTSTART:20260429T050000Z
DTEND:20260429T060000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/24
DESCRIPTION:by Muhammad  Afifurrahman (UNSW Sdyney) as part of UNSW Number
  Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\nAbstr
 act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Iyer (UNSW Sdyney)
DTSTART:20260415T040000Z
DTEND:20260415T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/25
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/UNSW-
 NTSeminar/25/">Cubic Polynomials and Sums of Two squares</a>\nby Siddharth
  Iyer (UNSW Sdyney) as part of UNSW Number Theory Seminar\n\nLecture held 
 in Room 4082\, Lawrence East (H13).\n\nAbstract\nWe establish a lower boun
 d for the frequency with which an irreducible monic cubic polynomial can b
 e expressed as a sum of two squares ($\\square_{2}$). This provides a quan
 titative answer to a question posed by Grechuk (2021) concerning the infin
 itude of such values. Our proof relies on a two-dimensional unit argument 
 and the arithmetic of degree six number fields. For example\, we show that
  if $h \\equiv 2 \\pmod{4}$\, then\n\n$$\n\\# \\{n : n^3+h \\in \\square_{
 2}\, \\ 1 \\leq n \\leq x \\} \\gg x^{1/3-o(1)}.\n$$\n\nThese arguments ma
 y be generalised to study the representation of irreducible monic cubic po
 lynomials by the quadratic form $x^2+ny^2$\, where $n \\in \\mathbb{N}$.\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Harvey (UNSW Sdyney)
DTSTART:20260513T040000Z
DTEND:20260513T050000Z
DTSTAMP:20260404T094802Z
UID:UNSW-NTSeminar/26
DESCRIPTION:by David Harvey (UNSW Sdyney) as part of UNSW Number Theory Se
 minar\n\nLecture held in Room 4082\, Lawrence East (H13).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UNSW-NTSeminar/26/
END:VEVENT
END:VCALENDAR