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BEGIN:VEVENT
SUMMARY:Aaron Manning (UNSW Sydney)
DTSTART:20250611T040000Z
DTEND:20250611T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/1/">Counting Matrices Over Finite Rank Multiplicative Groups</a>\nby Aa
 ron Manning (UNSW Sydney) as part of UNSW Number Theory Seminar\n\nLecture
  held in Room 4082\, Lawrence East (H13).\n\nAbstract\nThere have been man
 y recent works regarding arithmetic statistics questions related to matric
 es with entries from sets of number theoretic interest. This includes\, in
  particular\, providing upper bounds on the number of matrices with a pres
 cribed rank\, determinant\, or characteristic polynomial\, over such a set
 . Motivated by some recent work by Alon and Solymosi (2023)\, we consider 
 matrices with entries from finitely generated subgroups of the group of un
 its of a field of characteristic zero. Such sets require a considerably di
 fferent approach to many that have been studied previously. The primary to
 ols we require follow from the Subspace Theorem of Schmidt (1972) on the s
 imultaneous approximation of algebraic numbers by rational numbers.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Trudgian (UNSW Canberra)
DTSTART:20250611T050000Z
DTEND:20250611T060000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/2/">A convex hull\, a boundary drawn<br> Envelops points from dusk till
  dawn</a>\nby Timothy Trudgian (UNSW Canberra) as part of UNSW Number Theo
 ry Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract
 \nMany results in number theory rely on bounding exponential sums. The tit
 le (written\, like so many student assignments\, by ChatGPT) mentions a co
 nvex hull. The more we know about this set of points\, the better our know
 ledge of exponential sums. Applications abound! I will mention these and a
 n online database in which everyone can contribute\n\nhttps://github.com/t
 eorth/expdb\n\nall of which is joint work with Terry Tao and Andrew Yang.\
 n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Breuer (University of Newcastle)
DTSTART:20250625T040000Z
DTEND:20250625T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/3/">Coefficients of modular polynomials</a>\nby Florian Breuer (Univers
 ity 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 crypto
 graphy. Famously\, these polynomials have very large coefficients. In this
  talk I will outline some recent results on the sizes and divisibility pro
 perties of these coefficients. Time permitting\, I will also touch on the 
 analogous situation for Drinfeld modular polynomials.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryce Kerr (UNSW Canberra)
DTSTART:20250625T050000Z
DTEND:20250625T060000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/4/">Poissonian pair correlation for real sequences</a>\nby Bryce Kerr (
 UNSW Canberra) as part of UNSW Number Theory Seminar\n\nLecture held in Ro
 om 4082\, Lawrence East (H13).\n\nAbstract\nThe Poissonian pair correlatio
 n is a local statistic that captures strong pseudo-randomness in determini
 stic sequences. In a forthcoming paper with Lianf\, we provide new suffici
 ent conditions under which a real sequence exhibits the metric Poissonian 
 property. This will be a continuation of Liang’s talk a few weeks ago.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Harm (UNSW Sydney)
DTSTART:20250709T050000Z
DTEND:20250709T060000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/5/">Tackling the $\\varepsilon$ for primes in short arithmetic progress
 ions</a>\nby Michael Harm (UNSW Sydney) as part of UNSW Number Theory Semi
 nar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nGiven
  a zero-free region and an average zero-density estimate for all Dirichlet
  $L$-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. as
 sume the Generalized Density Hypothesis\, then as $x\\rightarrow \\infty$ 
 the prime number theorem holds for any arithmetic progression modulo $q\\l
 eq \\log^\\ell x$  for any $\\ell>0$ and in the interval $(x\,x+\\sqrt{x}\
 \exp(\\log^{2/3+\\varepsilon} x)]$ for any $\\varepsilon>0$. This refines 
 the classic interval $(x\,x+x^{1/2+\\varepsilon}]$.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Iyer (UNSW Sydney)
DTSTART:20250709T040000Z
DTEND:20250709T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/6/">Gaps between quadratic forms</a>\nby Siddharth Iyer (UNSW Sydney) a
 s part of UNSW Number Theory Seminar\n\nLecture held in Room 4082\, Lawren
 ce East (H13).\n\nAbstract\nLet $\\triangle$ denote the integers represent
 ed by the quadratic form $x^2+xy+y^2$ and $\\square_{2}$ denote the number
 s 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 $n \\i
 n \\triangle$\, and $n + a \\in \\square_{2}$. We conduct a census of $S(\
 \triangle\,\\square_{2}\,a)$ in short intervals by showing that there exis
 ts a constant $H_{a} > 0$ with\n$$\n\\# S(\\triangle\,\\square_{2}\,a)\\ca
 p [x\,x+H_{a}\\cdot x^{5/6}\\cdot \\log^{19}x] \\geq x^{5/6-\\varepsilon}\
 n$$\nfor large $x$. To derive this result and its generalization\, we util
 ize a theorem of Tolev (2012) on sums of two squares in arithmetic progres
 sions and analyse the behavior of a multiplicative function found in Blome
 r\, Brüdern & Dietmann (2009). Our work extends a classical result of Est
 ermann (1932) and builds upon work of Müller (1989).\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Badziahin (University of Sydney)
DTSTART:20250723T040000Z
DTEND:20250723T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/7/">Can we generate "RSA-safe" values of polynomials</a>\nby Dmitry Bad
 ziahin (University of Sydney) as part of UNSW Number Theory Seminar\n\nLec
 ture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nA crucial part 
 of various cryptosystems such as RSA is to generate composite numbers $n=p
 q$ that are almost impossible to factorise. Among other restrictions\, tha
 t means that n needs to be huge (e.g. 2048 bits) and $p$ and $q$ need to b
 e primes of a similar size. Such numbers are not difficult to generate. Bu
 t 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 $m$? Then the
  problem becomes much less trivial. In this talk I will discuss how one ca
 n randomly generate such triples $(p\,q\,m)$ for quadratic and cubic polyn
 omials $P$. We will also see that $p$ and $q$ can be generated in such a w
 ay that $p/q$ is close to any given positive real number.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shanta Laishram (Indian Statistical Institute\, New Delhi)
DTSTART:20250723T050000Z
DTEND:20250723T060000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/8/">On a class of Monogenic polynomials</a>\nby Shanta Laishram (Indian
  Statistical Institute\, New Delhi) as part of UNSW Number Theory Seminar\
 n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\nLet $f(x)
  \\in \\mathbb{Z}[x]$ be an irreducible polynomial of degree\n$n$ and $\\t
 heta$ be a root of $f(x)$. Let $K=\\mathbb{Q}(\\theta)$ be\nthe number fie
 ld and $\\mathbb{Z}_K$ be the ring of algebraic integers\nof $K$. We 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 consider 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 polynom
 ials having non\nsquare-free discriminant and Galois group $S_n$\, the sym
 metric group\non $n$ symbols. This is a joint work with A. Jakhar and P. Y
 adav.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis Combes (University of Sydney)
DTSTART:20250917T040000Z
DTEND:20250917T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/9/">Selmer groups for mod p Galois representations</a>\nby Lewis Combes
  (University of Sydney) as part of UNSW Number Theory Seminar\n\nLecture h
 eld in Room 4082\, Lawrence East (H13).\n\nAbstract\nSelmer groups are an 
 important construction in modern number theory\, with their ranks expected
  to encode arithmetic information associated to their underlying objects. 
 This is most obvious in conjectures like that of Bloch-Kato\, relating an 
 $L$-value to the rank of a Selmer group of a $p$-adic Galois representatio
 n. In recent years\, mod $p$ Galois representations have started to receiv
 e similar attention\, partly due to Scholze's proof that many torsion clas
 ses have their own associated representations. In this talk we will cover 
 some basics of Selmer groups\, how to compute them for mod $p$ Galois repr
 esentations\, and how to formulate and test interesting conjectures regard
 ing their ranks.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Fish (University of Sydney)
DTSTART:20250917T050000Z
DTEND:20250917T060000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/10/">Ehrhart spectra of large subsets in $\\Z^n$</a>\nby Alexander Fish
  (University of Sydney) as part of UNSW Number Theory Seminar\n\nLecture h
 eld in Room 4082\, Lawrence East (H13).\n\nAbstract\nThe Ehrhart spectrum 
 of a set $E$ in $\\Z^n$\, defined as the set of all Ehrhart polynomials of
  simplices with vertices in $E$\, generalizing the notion of volume spectr
 um. 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 Michae
 l Bjorkludn and Rickard Cullman both from Chalmers.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Afifurrahman (UNSW Sydney)
DTSTART:20251001T050000Z
DTEND:20251001T060000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/11/">Counting multiplicatively dependent integer vectors on a hyperplan
 e</a>\nby Muhammad Afifurrahman (UNSW Sydney) as part of UNSW Number Theor
 y Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nAbstract\
 nWe give several asymptotic formulas and bounds for the number of multipli
 cativly dependent integer vectors of bounded height that lies on a hyperpl
 ane\, extending the work of Pappalardi\, Sha\, Shparlinski and Stewart. Jo
 int work with Valentio Iverson and Gian Cordana Sanjaya  (University of Wa
 terloo).\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bittu Chahal (IIIT Delhi)
DTSTART:20251001T040000Z
DTEND:20251001T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/12/">Chebyshev's bias for irrational factor function</a>\nby Bittu Chah
 al (IIIT Delhi) as part of UNSW Number Theory Seminar\n\nLecture held in R
 oom 4082\, Lawrence East (H13).\n\nAbstract\nChebyshev's bias is the pheno
 menon that the number of prime quadratic nonresidues of a given modulus pr
 edominate over the prime quadratic residues\, in other words\, primes are 
 biased toward quadratic nonresidues. We study this bias question in the co
 ntext of the irrational factor function $I_k(n)$\, defined by $I_k(n)=\\pr
 od_{i=1}^lp_i^{\\beta_i}$\, where $n=\\prod_{i=1}^lp_i^{\\alpha_i}$ and \n
 $$\\beta_i=\n\\left\\{\\begin{array}{cc}\n   \\alpha_i\,  & \\textrm{if } 
  \\alpha_i < k\,\\\\ \n   \\frac{1}{\\alpha_i}\,   & \\textrm{if } \\alpha
 _i\\geq k.\\end{array}\\right.$$\nIn particular\, we introduce the irratio
 nal factor function in both number field and function field settings\, der
 ive asymptotic formulas for their average value\, and establish $\\Omega$-
 results for the error term in the asymptotic formulas. Furthermore\, we st
 udy the Chebyshev's bias phenomenon for number field and function field an
 alogues of sum of the irrational factor function\, under assumptions on th
 e real zeros of Hecke $L$-functions associated with Hecke characters in th
 e number field case.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liangyi Zhao (UNSW Sydney)
DTSTART:20251015T030000Z
DTEND:20251015T040000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/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\, Lawrence Eas
 t (H13).\n\nAbstract\nGrey\, dear friends\, is all unproven theory.  Thus 
 I mar the immortal words of a very witty and most unjustly abused immortal
 .  At the most recent meeting of Number Theory Down Under\, it was suggest
 ed that the work of Kerr-Shparlinski-Wu-Xi on Kloosterman sums might be ap
 plied to improve an asymptotic formula of Gao-Zhao for the twisted fourth 
 moment of Dirichlet $L$-functions to certain prime power moduli\, as 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 untest
 ed theory.  More specifically\, taking the above recommendation\, as 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\, during thi
 s talk.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chiara Bellotti (UNSW Canberra)
DTSTART:20251015T040000Z
DTEND:20251015T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/14/">A New Zero-Density Estimate for the Riemann Zeta Function close to
  the $1$-line</a>\nby Chiara Bellotti (UNSW Canberra) as part of UNSW Numb
 er Theory Seminar\n\nLecture held in Room 4082\, Lawrence East (H13).\n\nA
 bstract\nIn this talk we present a new type of zero-density estimate for t
 he Riemann zeta function close to the one-line. In particular\, we show th
 at the number of zeros in this region remains bounded by an absolute const
 ant when approaching the left edge of the Korobov–Vinogradov zero-free r
 egion. As a consequence\, we obtain an essentially optimal refinement of a
  result due to Pintz concerning the error term in the prime number theorem
 .\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youming Qiao (University of Technology Sydney)
DTSTART:20251029T040000Z
DTEND:20251029T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/15/">A quantum algorithm for $2\\times 2\\times 2$ tensor isomorphism o
 ver $\\mathbb{Z}$</a>\nby Youming Qiao (University of Technology Sydney) a
 s part of UNSW Number Theory Seminar\n\nLecture held in Room 4082\, Lawren
 ce East (H13).\n\nAbstract\nWe present a quantum polynomial-time algorithm
  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 $\\
 mathrm{GL}(2\, \\mathbb{Z})\\times\\mathrm{GL}(2\, \\mathbb{Z})\\times\\ma
 thrm{GL}(2\, \\mathbb{Z})$. This algorithm is a natural consequence of the
  works of Gauss (on composition laws)\, Bhargava (on higher composition la
 ws)\, and Hallgren (on quantum algorithms for the principal ideal problem)
 . An intriguing question is the case of $\\mathbb{Z}^3\\otimes\\mathbb{Z}^
 3\\otimes\\mathbb{Z}^3$.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Ward (University of York)
DTSTART:20251105T030000Z
DTEND:20251105T040000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/16/">Sets of Exact(er) approximation order</a>\nby Benjamin Ward (Unive
 rsity of York) as part of UNSW Number Theory Seminar\n\nLecture held in Ro
 om 4082\, Lawrence East (H13).\n\nAbstract\nIn this talk\, which is joint 
 work with Simon Baker (Loughborough\, UK)\, I will introduce a quantitativ
 e notion of exactness within Diophantine approximation. Given functions Ψ
  : (0\, ∞) → (0\, ∞) and ω : (0\, ∞) → (0\, 1)\, we study the s
 et of points that are Ψ-well approximable but not Ψ(1 − ω)-well appro
 ximable\, denoted E(Ψ\,ω). This generalises the set of Ψ-exact approxim
 ation order as studied by Bugeaud (Math. Ann. 2003). We prove results on t
 he cardinality and Hausdorff dimension of E(Ψ\,ω). In particular\, for c
 ertain 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 multip
 lied by a constant. The results discussed can be found in [2510.18451] A q
 uantitative framework for sets of exact approximation order by rational nu
 mbers.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Subham Bhakta (UNSW Sydney)
DTSTART:20251105T040000Z
DTEND:20251105T050000Z
DTSTAMP:20260314T090757Z
UID:UNSW-NTSeminar/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/17/">Character sums with division polynomials of elliptic curves</a>\nb
 y Subham Bhakta (UNSW Sydney) as part of UNSW Number Theory Seminar\n\nLec
 ture 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 polyno
 mials evaluated at rational points on elliptic curves over prime fields\; 
 a topic that first caught my attention near the end of my PhD\, inspired b
 y a 2009 paper of I. E. Shparlinski and K. E. Stange. These character valu
 es exhibit an “almost multiplicative” behaviour. Motivated by Chowla
 ’s conjectures on correlations of multiplicative functions\, I will firs
 t present a recent joint work with I. E. Shparlinski (2025) on the correla
 tions of these character sums under shifts. I will then discuss some bound
 s for these sums when twisted by various multiplicative functions.\n
LOCATION:https://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:20260314T090757Z
UID:UNSW-NTSeminar/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNSW-NTSemin
 ar/18/">Numerical verification of the Collatz Conjecture</a>\nby Andreas-S
 tephan Elsenhans (University of Sydney and University of Würzburg) as par
 t of UNSW Number Theory Seminar\n\nLecture held in Room 4082\, Lawrence Ea
 st (H13).\n\nAbstract\nThe Collatz conjecture (also known as the 3n+1 prob
 lem) is one of the most\npopular open problems in number theory. In this t
 alk I will give an introduction to \na theoretical analysis of the problem
  and explain which strategies are used for\na numerical verification.\n
LOCATION:https://researchseminars.org/talk/UNSW-NTSeminar/18/
END:VEVENT
END:VCALENDAR