Date/Time : 15 Sep 2021 16:00
Venue : via Zoom
Speaker : Bakhadyr Khoussainov, UESTC, Chengdu and The University of Auckland

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

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

Abstract: This talk belongs to the area of probabilistic logic semantics.

The first contribution of this work is the introduction of probability structures. Probability structures are the algebraic structures equipped with probability functions on the domains and the atomic predicates. These structures extend type 1 probability structures introduced by Halpern and Bacchus.

Type 1 probability structures contain probability functions on domains only. Our probability structures possess an additional statistical knowledge, – probability functions on atomic predicates.

We present a method that builds probability spaces for the first order logic formulas and prove that our semantics is sound.

The second contribution of this work is the introduction of smooth probability structures.

The smooth probability structures carefully refine probability structures so that we have a better control of the probability spaces defined by first order logic formulas. For these structures we initiate the study of first order probability logic (FOPLS), investigate axiomatizability of FOPLS, and address decidability and undecidability questions of the sets of valid formulas. We also study a few algorithmic questions on probability structures.

The work is joint with Mingyu Xiao (UESTC) and Jiamou Liu (The University of Auckland).

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Date/Time : 10 Sep 2021 09:00
Venue : via Zoom
Speaker : YanYan Li, Rutgers University

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https://nus-sg.zoom.us/j/84328425455?pwd=MXpPQWYxZ0hvQ2UzOW1sbUREUG5XZz09

Meeting ID: 843 2842 5455
Passcode: 204458

Abstract:  We will first recall the Nirenberg problem and the Yamabe problem, together with some previous results on the existence and compactness of solutions to the problems. We will then discuss the σ_k-Nirenberg problem and the σ_k-Yamabe problem, the study of which requires solving fully nonlinear elliptic equations involving Schouten tensor on Riemannian manifolds. Some recent works and open problems will be discussed.

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Date/Time : 10 Sep 2021 15:00
Venue : via Zoom
Speaker : Emile Takahiro Okada, University of Oxford

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https://nus-sg.zoom.us/j/82201157603?pwd=WktRRC9hbHFsaFR6VlF6amdGNk5tZz09

Meeting ID: 822 0115 7603
Passcode: 509310

Abstract:  The wavefront set is a powerful invariant which one can attach to representations of reductive groups over both global and local fields. Notably there is a non-trivial interplay between the wavefront set of an automorphic representation and that of its local factors. In this talk we will discuss recent results computing the wavefront set for all spherical Arthur representations in the p-adic case and the new techniques used in the computation.

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Date/Time : 08 Sep 2021 16:00
Venue : via Zoom
Speaker : Duc-Manh Nguyen, University of Bordeaux

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Since the work of Eskin-Okounkov in 2001, it has been known that in any stratum of translation surfaces, the number of square-tiled surafces constructed from at most n squares grows like $c\pi^{2g}n^d$, where $d$ is the (complex) dimension of the stratum, $g$ is the genus of the surfaces, and $c$ is a rational number. Similar phenomena also occur in strata of quadratic differentials. Counting square-tiled surfaces in a given stratum is more or less the same as counting quadrangulations of a topological surface, with some constraints on the singularities and the holonomy of the associated flat metric. More recently, Engel showed that the asymptotics of the numbers of quadrangulations and triangulations with at most $n$ tiles are of the form $\alpha n^d$, where $\alpha$ is a constant in $Q[\pi]$ or $Q[\sqrt{3}\pi]$. In this talk, we will explain how the asymptotics above is related to the volume of some moduli spaces. Moreover, in some situations they can be computed from the self-intersection number of a divisor in some complex projective varieties. This implies in particular that the constant $\alpha$ belongs actually to either $Q\cdot\pi^d$, or  $Q\cdot(\sqrt{3}\pi)^d$ in those cases. This is joint work with Vincent Koziarz.

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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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