Date/Time : 08 Sep 2021 16:00
Venue : via Zoom
Speaker : Bakhadyr Khoussainov / Frank Stephan, UESTC, Chengdu and The University of Auckland, New Zealand / NUS

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Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Parity games are games where a marker is moved on a finite graph and each node is annotated with a natural number; the game runs forever and the largest number in an infinitely often visited node decides the winner, if it is even then player Anke wins else player Boris wins. Marcin Jurdzinski showed that this game is in UP intersected coUP and also provided the first not fully exponential algorithm for it; however, the exact time complexity remained unresolved. In 2017, Calude, Jain, Khoussainov, Li and Stephan found a quasipolynomial time algorithm which Jurdzinski and Lazic as well as Schewe and his collaborators improved to be in polynomial space as well. The talk provides the way this algorithm was found and the implications it has for the fixed-parameter-tracktability of parity games and related problems like coloured Muller games. Though now quite a number of quasipolynomial time algorithms are known and there is quite extensive research in this topic, the question on whether parity games can even be solved in polynomial time is still unresolved.

This talk is given by Bakhadyr Khoussainov and Frank Stephan jointly also on behalf of their coauthors Cristian Calude, Sanjay Jain and Wei Li.

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Date/Time : 01 Sep 2021 14:00
Venue : via Zoom
Speaker : Yongqi Feng, Shantou University

Join Zoom Meeting https://nus-sg.zoom.us/j/89953315552?pwd=bERiQUVLSEhPNlFsRWNIR21qWGZOQT09 Meeting ID: 899 5331 5552 Passcode: 911014 Let k be a non-archimedean local field, and let G be a connected reductive k-group which splits over an unramified extension of k. Hiraga, Ichino and Ikeda conjectured that the formal degree d(π) of a discrete series representation π of G(k) can be computed via the associated discrete (i.e. elliptic) local Langlands parameter (φπ, ρπ). The supercuspidal unipotent representations form a convenient class to test this conjecture, with known classification and formal degrees when G is simple and adjoint. We shall discuss, for supercuspidal unipotent representations of classical groups, the proof of the HII formal degree conjecture. This leads to a local Langlands correspondence for such representations, which agrees with the parametrization obtained by Morris and Lusztig when G is simple and adjoint. This is joint-work with Eric Opdam and Maarten Solleveld.

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Date/Time : 01 Sep 2021 16:00
Venue : via Zoom
Speaker : Rupert Hoelzl, Bundeswehr University Munich

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 We investigates inductive inference from the perspective of reverse mathematics. Reverse mathematics is a framework that allows gauging the proof strength of theorems and axioms in many areas of mathematics. We apply its methods to basic notions of algorithmic learning theory such as Angluin’s tell-tale criterion and its variants for learning in the limit and for conservative learning, as well as to the more general scenario of partial learning. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to induction strength and to domination of weakly represented families of functions. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

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Date/Time : 01 Sep 2021 16:00
Venue : via Zoom
Speaker : Elisha Falbel, Mathematics Institute of Jussieu–Paris Rive Gauche (IMJ-PRG)

Join Zoom Meeting https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09 Meeting ID: 875 1147 6637 Passcode: 468399 A path structure on a three-manifold is a contact structure (with fixed contact form) with a choice of two directions on each contact plane. It appears, for instance, in the theory of Anosov flows. I will explain how to classify such structures on a compact manifold with a large automorphism group extending a classification result of Ghys for Anosov flows. This is joint work with M. Mion-Mouton and J. M. Veloso.

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Date/Time : 27 Aug 2021 09:00
Venue : via Zoom
Speaker : Yufei Zhao, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/87977920058?pwd=R1FxeXJHeGVGeHQ5RGhYR0xwOXVsZz09 Meeting ID: 879 7792 0058 Passcode: 458785 Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle. A key ingredient is a new result in spectral graph theory: the adjacency matrix of a connected bounded degree graph has sublinear second eigenvalue multiplicity. My talk will discuss these problems and their connections, along with extensions and open problems (e.g., what is the maximum possible second eigenvalue multiplicity of a connected bounded degree graph?). Joint work with Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang.

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Date/Time : 25 Aug 2021 16:00
Venue : via Zoom
Speaker : Ng Keng Meng,

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 There has been a recent revival in the interest in sub-computable mathematics. One of these approaches is to consider “primitive recursive” or punctual structures. This has led to a greater understanding in the effective content of well-known objects and proofs in classical computability theory. When considering the punctual anaologies of classical computabilitiy we often obtain strange and surprising results. I will discuss some recent work in progress in this area, focussing particularly on structural results. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html  

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Date/Time : 25 Aug 2021 14:00
Venue : via Zoom
Speaker : Korkeat Korkeathikhun, University of North Carolina, Chapel Hill

Join Zoom Meeting https://nus-sg.zoom.us/j/89816394951?pwd=OXRvc1pXY0kxSGhYRkloMnFkL0dSUT09 Meeting ID: 898 1639 4951 Passcode: 903999 Let $G$ be a simply-connected simple algebraic group, $\mathfrak{g}$ its Lie algebra. Let $\mathrm{Gr}_G$ be the affine Grassmannian of $G$, and $\mathrm{Gr}_0^-$ the opposite open Schubert cell in $\mathrm{Gr}_G$. Achar and Henderson defined a map $\pi:\mathrm{Gr}_0^- \to \mathfrak{g}$ and used it to exhibit the relation between Schubert varieties in $\mathrm{Gr}_G$ and nilpotent cone in $\mathfrak{g}$. In our work, we consider a twisted analouge. We relate the geometry of Schubert varieties in twisted affine Grassmannian and the nilpotent varieties in symmetric spaces. This extends some results of Achar-Henderson in the twisted setting. We also get some applications for the geometry and topology of the order 2 nilpotent varieties in certain classical symmetric spaces.

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Date/Time : 18 Aug 2021 14:00
Venue : via Zoom
Speaker : Jinfeng Song, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/82727387952?pwd=WEo0M0lsd0tETHdhZWZIRGJUaEhEUT09 Meeting ID: 827 2738 7952 Passcode: 557651 Any variety over a field of characteristic p>0 possesses a Frobenius endomorphism F, which fixes all the points and raises the function to p-th power. A variety X is called Frobenius split if the p-th power map splits as a morphism of sheaves of modules. The most important class of examples of varieties which are Frobenius split are flag varieties. This is firstly proved by Mehta and Ramanathan using geometric methods. Later, Kumar and Littelmann construct an alternative proof using the methods of quantum groups. In this talk, I plan to introduce Kumar and Littelmann’s method, and explain its potential generalisation to quantum symmetric pairs.

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Date/Time : 18 Aug 2021 16:00
Venue : via Zoom
Speaker : Yu Liang, Nanjing University

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 Besicovitch-Davis theorem says that the Hausdorff dimension of every analytic set can be approximated by its closed subset. But the Besicovitch-Davis theorem fails for co-analytic sets under the assumption V=L as observed by Slaman. We prove that the theorem holds for arbitrary sets under ZF+sTD. We also prove that the theorem holds for Sigma-1-2-sets under Martin’s axiom. This is joint work with Peng Yinhe and Wu Liuzhen.

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