Date/Time : 09 Oct 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Ho Boon Suan, National University of Singapore

When traversing a graph, each subsequent node is typically chosen from the set of unvisited nodes adjacent to the already visited ones. In this talk, I will explore how to count the number of possible traversals, particularly in graphs with a lot of symmetry. We will see how these counting problems lead to interesting hypergeometric identities and how computational methods can help in establishing such identities. The talk is intended for a general mathematical audience.

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Date/Time : 09 Oct 2024 17:00
Venue : S17 #04-04 (SR3)
Speaker : Athipat Thamrongthanyalak, Chulalongkorn University

In this talk, we study a converse of the Banach fixed point theorem and its connection to tameness in expansions of a real closed field. Let R be a definably complete expansion of a real closed field.

We say that R has the BFPP (short for, Banach fixed point property) when, for every locally closed definable set E, if every contraction on E has a fixed point, then E is closed. In this talk, we prove that if R has an o-minimal open core, then R has the BFPP; and if R has the BFPP, then R has a locally o-minimal open core.

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Date/Time : 03 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Dihua Jiang, University of Minnesota

I will discuss relations between non-abelian Fourier transforms and the Langlands conjecture on automorphic L-functions and associated local factors in the framework of Braverman-Kazhdan-Ngo.

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Date/Time : 03 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Meng Fai Lim, Central China Normal University

In this talk, we begin reviewing the non-commutative Iwasawa theory as developed by Coates, Fukaya, Kato, Sujatha and Venjakob which is concerned with attaching suitable characteristic elements to modules of arithmetic interest (for instance, Selmer groups). By their construction, these characteristic elements are realized as element in an appropriate localized K_1 group. We then introduce a notion of “taking modulo p” of these characteristic elements and discuss some of its properties. This is an ongoing work with Chao Qin.

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Date/Time : 02 Oct 2024 14:00
Venue : via Zoom
Speaker : Jing Yu, Fudan University

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Meeting ID: 810 4646 2775
Passcode: 23571113

In 1995, Levin and Linial, London, and Rabinovich conjectured that every connected graph $G$ of polynomial growth admits an injective homomorphism to the $n$-dimensional grid graph for some $n$. Moreover, they conjected that if every ball of radius $r$ in $G$ contains at most $O(r^\rho)$ vertices, then one can take $n = O(\rho)$. Krauthgamer and Lee confirmed the first part of this conjecture and refuted the second in 2007. By constructing some finite expander graphs, they showed best possible upper bound on $n$ is $O(\rho \log \rho)$.

Prompted by these results, Papasoglu asked whether a graph $G$ of polynomial growth admits a coarse embedding into a grid graph. We give an affirmative answer to this question. Moreover, it turns out that the dimension of the grid graph only needs to be linear in the asymptotic growth rate of $G$, which confirms the original Levin–Linial–London–Rabinovich conjecture “on the large scale.”

Besides, we find an alternative proof of the result of Papasoglu that graphs of polynomial growth rate $\rho < \infty$ have asymptotic dimension at most $\rho$.

Furthermore, our proof works in the Borel setting and shows that Borel graphs of polynomial growth rate $\rho < \infty$ have Borel asymptotic dimension at most $\rho$.

(This is joint work with Anton Bernshteyn.)

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Date/Time : 02 Oct 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Hideo Kojima, Niigata University

A cuspidal curve means a projective curve whose singular points are locally irreducible. The study of rational cuspidal plane curves has had a long and interesting history. In the first half of the talk, I will introduce some of recent progress on the study. Then, I will give some results on rational cuspidal curves on Q-homology projective planes. Here, a Q-homology plane is a normal projective complex surface with quotient singularities having the same rational homology as the projective plane. Some results on rational cuspidal plane curves will be generalized.

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Date/Time : 25 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Hsuan-Tien Lin, National Taiwan University

Complementary-Label Learning (CLL) is a weakly supervised learning paradigm that is claimed to be useful in situations where collecting true labels is expensive. This talk begins by walking the audience through two advances in CLL. The first work discovered that the CLL loss design from Unbiased Risk Estimator (URE) suffers from high variance in gradient estimation. To address this, a novel surrogate complementary loss (SCL) framework is proposed, which reduces variance and improves gradient alignment, mitigating the overfitting issue. The second work introduces a new approach to CLL by reducing the problem to estimating the probability of complementary classes. This framework sidesteps the limitations of traditional methods and improves robustness in noisy environments, offering a broader perspective for both deep and non-deep models. Empirical results demonstrate the efficacy of both approaches in improving CLL performance. Finally, the speaker will share some of the ongoing attempts in making CLL more realistic, including some first-hand experience in collecting real-world datasets and releasing an open-source library.

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Date/Time : 23 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : David Schwein, University of Bonn

Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem, solved when p is large. When p is small, the remaining supercuspidals are expected to have an arithmetic source: wildly ramified field extensions. In this talk I’ll discuss ongoing work joint with Jessica Fintzen that identifies a second, Lie-theoretic, source of new (tame!) supercuspidals: special features of root systems at very small primes.

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Date/Time : 18 Sep 2024 12:00
Venue : via Zoom
Speaker : Peter van Hintum, Institute for Advanced Study

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https://nus-sg.zoom.us/j/81046462775?pwd=aDhaYnhQOTgybzdYS21yajlQdnBmZz09

Meeting ID: 810 4646 2775
Passcode: 23571113

The Brunn-Minkowski inequality is a foundational result in convex geometry asserting that if sets A and B in R^n have the same volume and t is some number in (0,1), then |tA+(1-t)B|>|A|. We’ll prove the following folklore conjecture on the stability of the Brunn-Minkowski inequality that if in fact |tA+(1-t)B|<(1+d) |A|, then there is a common convex hull K containing A and B so that |K|<(1+ O(sqrt(d)))|A| and |co(A)|<(1+O(d))|A|. We’ll additionally describe how this result neatly fits in the additive combinatorics study of sets with small sumset. (based on joint work with Alessio Figalli and Marius Tiba)

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