Date/Time : 13 Apr 2023 10:00
Venue : via Zoom
Speaker : Daniel Sanz-Alonso, University of Chicago

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Meeting ID: 812 6121 0349
Passcode: 557052

Semi-supervised learning refers to the problem of recovering an input-output map using many unlabeled examples and a few labeled ones. In this talk I will survey several mathematical questions arising from the Bayesian formulation of graph-based semi-supervised learning. These questions include the modeling of prior distributions for functions on graphs, the derivation of continuum limits for the posterior, the design of scalable posterior sampling algorithms, and the contraction of the posterior in the large data limit.

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Date/Time : 12 Apr 2023 16:00
Venue : via Zoom
Speaker : Tran Chieu-Minh, National University of Singapore

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Meeting ID: 810 4646 2775
Passcode: 23571113

The following question was described in Ben Green’s list of open problems, but also attributed to discussions with Emmanuel Breuillard: When A \subseteq SO(3, R) has sufficiently small normalized Haar measure, do we have \mu(AA) > 3.99 \mu(A)?
This problem is often considered the first serious obstacle in generalizing results of additive combinatorics to nonabelian settings when we also want sharp bounds.

In this talk, I will discuss a recent joint work with Jing Yifan and Zhang Ruixiang where we combine techniques from model theory, probability theory, and harmonic analysis to answer it positively.

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Date/Time : 12 Apr 2023 17:00
Venue : via Zoom
Speaker : Daniel Max Hoffmann, University of Warsaw

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Date/Time : 06 Apr 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Quan Zhao, University of Regensburg, Germany

In this talk, I will consider the structure-preserving front-tracking methods for a sharp-interface model of two-phase flow in both the unfitted and fitted mesh approaches, meaning that the volume preservation and energy decay are satisfied on the discrete level. In the unfitted approach, the constructed method is based on an Eulerian weak formulation, while in the fitted approach, the method is devised in the arbitrary Lagrangian-Eulerian (ALE) framework. We compare the numerical results of the two approaches by using the example of a rising bubble.

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Date/Time : 06 Apr 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Nadya Gurevich, Ben Gurion University of the Negev

The classical Schur-Weyl duality, relating representations of the symmetric group S(r) and of sl(n), admits a quantum affine generalization. We explain its relation to the Whittaker functor on the category of Iwahori-spherical genuine representations of a central cover of GL(r) of degree n. 

In particular, we deduce that the space of Whittaker functionals on such representation admits an action of an affine quantum group.

This is a joint work with Fan Gao and Edmund Karasiewicz.

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Date/Time : 05 Apr 2023 17:00
Venue : S17 #05-11 (SR5)
Speaker : Frank Stephan, National University of Singapore

Languages over the unary alphabet have been studied in computer science for a long time. The present work investigates regular languages over the unary alphabet and one investigates the various forms of representing them by finite automata. Here three types of automata are studied:

(a) Deterministic finite automata where the finite automaton has exactly one run per word which is accepting iff the word is in the given language.

(b) Nondeterministic finite automata where there are choices in the states on how to procede with a run on various symbols, a word is in the language iff there is some run which is accepting.

(c) Unambiguous finite automata which are a special case of nondeterministic finite automata and which either reject a word or which have exactly one accepting run for a word.

The results presented are from the following two areas:

(1) This paper improves the upper bound of the equality problem of unary nondeterministic automata from an exponential in the second root to an exponential in the third root of the number of states. This almost matches a known lower bound based on the exponential time hypothesis by Fernau and Krebs.

(2) It is established that the standard regular operations of union, intersection, complementation and Kleene star cause either only a polynomial or a quasipolynomial blow-up.
Concatenation of two n-state ufas, in worst case, causes a blow-up from n to a function with an exponent of sixth root of n. Decision problems of finite formulas using regular operations and comparing languages given by n-state unambiguous automata, in worst case, require an exponential-type of time under the Exponential Time hypothesis and this complexity goes down to quasipolynomial time in the case that the concatenation of languages is not used in the formula. Merely comparing two languages given by n-state ufas in Chrobak Normal Form is in LOGSPACE.

This talk is joint work with Gordon Hoi, Sanjay Jain and Christopher Tan.

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Date/Time : 05 Apr 2023 16:00
Venue : via Zoom
Speaker : Noam Lifshitz, Hebrew University

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Meeting ID: 810 4646 2775
Passcode: 23571113

A subset A of a group is said to be product free if for all elements a, b in A their product ab is not in A. In 1985 Babai and Sos posed the problem of determining the largest product free sets in the alternating group. We solve this problem completely when n is sufficiently large.

Our proof combines representation theory with a recent machinery we developed called `hypercontractvity for global functions’.

Based on joint works with Keevash, Long, and Minzer.

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Date/Time : 04 Apr 2023 16:00
Venue : via Zoom
Speaker : Johannes Flake, MPIM Bonn

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Meeting ID: 864 4631 5086
Passcode: 280937

I will explain a construction of categories with a tensor product using topological operations involving manifolds, or more precisely, cobordisms. Then I will show how to analyze categories like these using algebraic and representation-theoretic ideas. The categories in question include Deligne’s interpolation categories and Khovanov-Sazdanovic’s cobordism categories. We will discuss their Grothendieck rings and, if time permits, their monoidal centers.

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Date/Time : 03 Apr 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Xuhua He, Chinese University of Hong Kong

An invertible matrix is called totally positive if all its minors are positive. In 1994, Lusztig developed the theory of total positivity for arbitrary split real reductive groups and their flag manifolds. He further generalized the theory to arbitrary Kac-Moody groups in 2019. The theory of total positivity has found important applications in different areas: cluster algebras, higher Teichmuller theory, the theory of amplituhedron in physics, etc.

In this talk, we will discuss some remarkable combinatorial, geometric and representation-theoretic aspects of total positivity. This talk is based on some recent works with Huanchen Bao.

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