Date/Time : 18 Nov 2020 16:00
Venue : via Zoom
Speaker : Yu Yue Tony, Universit Paris-Saclay (Paris-Sud)

Join Zoom Meeting https://nus-sg.zoom.us/j/81669932092?pwd=WSt6V01ESFFpY0dVRnhVdEt3cUIrQT09 Meeting ID: 816 6993 2092 Password: 287641 Abstract:  Mirror symmetry is one of the most mysterious dualities in mathematics. My research explores a new approach to mirror symmetry, via non-archimedean geometry. I will give an overview of the recent progress in this direction. I will talk about non-archimedean enumerative geometry, the Frobenius structure conjecture, and derived non-archimedean geometry. I will also describe an application towards cluster algebras, and another application towards the moduli space of Calabi-Yau pairs.

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Date/Time : 18 Nov 2020 09:00
Venue : via Zoom
Speaker : Pablo Alvarez, Institute for Advanced Study

Join Zoom Meeting https://nus-sg.zoom.us/j/89214308777?pwd=VmZBVmZaamF5Z1h5VnU1MERaZ2ZVQT09 Meeting ID: 892 1430 8777 Password: 369675 Abstract:  The question of the center of the quantum group at a generic parameter was understood by Drinfeld in 1989, but the center of this algebra when you specialize at a root of unity remained an open question. By work of Lachowska, Qi and Bezrukavnikov we had some description of the center of the small quantum group. In joint work with Bezrukavnikov, Shen and Vasserot, we prove a more concrete description of the center of the small quantum group, in terms of the cohomology of a certain affine Springer fiber. In joint work with Kivinen and Losev, we link certain questions of the center in Type A with the Hilbert scheme of points on C2.

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Date/Time : 17 Nov 2020 09:00
Venue : via Zoom
Speaker : Huang Hao, Emory University

Join Zoom Meeting https://nus-sg.zoom.us/j/86270578593?pwd=cTYreG1hQlExWHJERStZN0hUWjNWQT09 Meeting ID: 862 7057 8593 Password: 313348 Abstract:  The biclique partition number bp(G) is the minimum number of complete bipartite graphs needed to partition the edges of a graph G. Its study was initiated in 1972 by Graham and Pollak, who showed that the complete graph with n vertices has biclique partition number exactly n-1. Since then, this important graph parameter has found many connections with problems arising from discrete geometry, communication complexity and network addressing. In this talk we will explore some of these connections and discuss counterexamples to two decade-old conjectures: one of Alon, Saks, and Seymour in 1991 saying the biclique partition number is strictly greater than the chromatic number; and another one of Erdos from the ’80s on random graphs. At the end of this talk, we will also outline the significance of studying its generalization for hypergraphs.

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Date/Time : 17 Nov 2020 16:00
Venue : via Zoom
Speaker : Çağrı Sert , University of Zürich, Switzerland

Join Zoom Meeting https://nus-sg.zoom.us/j/86006972904?pwd=Wm9vWWFHMEUxc3l3aHIrZDMyRlN0Zz09 Meeting ID: 860 0697 2904 Password: 071999 Abstract: In a first part, we will provide a (biased) overview of the theory of random matrix products. In a second part, we will focus on large deviation principle type results in that theory and mention some recent results as well as open questions. In the last part, we will shift to random compositions of isometries of hyperbolic spaces where some of the questions/results mentioned in the first part can be answered/proved differently with geometric methods. Based on joint work with Boulanger, Mathieu, Sisto.

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Date/Time : 12 Nov 2020 10:00
Venue : via Zoom
Speaker : Chengze Duan, University of Maryland, college park

Join Zoom Meeting https://nus-sg.zoom.us/j/85957375797?pwd=clE4UTk1WDF0VGMzdU5wVldIMnl2UT09 Meeting ID: 859 5737 5797 Password: 456131 Abstract:  n Vinberg’s study of characterization of reductive algebraic monoids and Vinberg monoids, he introduced the notion of perfect submonoids of dominant weights. Given a reductive algebraic monoids, we shall see a perfect submonoids of dominant weights of the group of units. Meanwhile, the perfect submonoids of dominant weights can also appears naturally from the tensor product decomposition in representation theory. We will see some explicit descriptions of the perfect submonoids of dominant weights and compare it with Vinberg’s results on reductive monoids.

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Date/Time : 11 Nov 2020 09:00
Venue : via Zoom
Speaker : Yu Hui, Columbia University

Join Zoom Meeting https://nus-sg.zoom.us/j/85408305509?pwd=OHpHQkdtUSt3YzdLN1BTVkxOeTRXQT09 Meeting ID: 854 0830 5509 Password: 843914 Abstract:  The N-membrane problem is the study of shapes of elastic membranes being pushed against each other. The main questions are the regularity of the functions modeling the membranes, and the regularity of the contact regions between consecutive membranes. These are classical questions in free boundary problems. However, very little is known when N is larger than 2. In this case, there are multiple free boundaries that cross each other, and most known techniques fail to apply. In this talk, we discuss, for general N, the optimal regularity of the solutions in arbitrary dimensions, and a classification of blow-up solutions in 2D. Then we focus on the regularity of the free boundaries when N=3. We also discuss how the techniques developed here can be applied to other problems involving multiple free boundaries. This talk is based on two recent joint works with Ovidiu Savin (Columbia University).

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Date/Time : 11 Nov 2020 17:00
Venue : via Zoom
Speaker : Philipp Schlicht, University of Vienna

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract:  Similarities between c.e., Pi^1_1 and Sigma^1_2 sets can be explained by representing Pi^1_1 and Sigma^1_2 sets as c.e. with respect to a transfinite enumeration procedure. This representation is important for classical results about Pi^1_1 and Sigma^1_2 sets, but also for recent results, for instance about randomness at the level of Pi^1_1 by Hjorth and Nies and structural results about Sigma^1_2 sets by Chong, Wu and Yu. In the main result, we calculate the lengths of enumerations. More precisely, we isolate a certain countable ordinal tau and show that the length of an enumeration of a Pi^1_1 or Sigma^1_2 set either equals omega_1 or is below tau, and tau is optimal. This ordinal has many other interesting characterisations. For example, we show that tau is the optimal bound for the countable ranks of wellfounded Sigma^1_2 relations, in analogy with the Kunen-Martin theorem. We will further touch on related structural problems such as calculating Borel ranks of Pi^1_1 and Sigma^1_2 Borel sets. This is joint work with Philip Welch and Merlin Carl.

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Date/Time : 11 Nov 2020 14:00
Venue : via Zoom
Speaker : Zhu Chengbo, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/89815068389?pwd=UXpnNXFNczNvTzhza3BqTVRHTllBQT09 Meeting ID: 898 1506 8389 Password: 543629 Abstract:  The idea that the study of finite dimensional representations of compact Lie groups amounts to the study of rational representations of reductive algebraic groups can be traced back to Hermann Weyl in the 1930’s. It was I.M. Gelfand who advocated that infinite-dimensional representations of non-compact Lie groups should be investigated by methods of functional analysis, and more specifically theory of distributions, in his ICM Plenary Lecture in 1954 (Some aspects of functional analysis and algebra) and in the six-volume work by I.M. Gelfand et al. on “Generalized Functions” (1960’s). Through two angles, I will explain why one needs to and how one applies, the theory of distributions. 1. Models of representations of the group SL(2,R); 2. Basic invariants of smooth representations: matrix coefficients and characters

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Date/Time : 11 Nov 2020 16:00
Venue : via Zoom
Speaker : Cai Zhenning, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83949543700?pwd=MVBqSlBTaUtwRmxWRndta0NZZ2tFZz09 Meeting ID: 839 4954 3700 Password: 380740 Abstract: The complex Langevin (CL) method is a numerical approach to alleviate the numerical sign problem in the computation of path integrals in lattice field theories. Mathematically, it is a simple numerical tool to compute a wide class of high-dimensional and oscillatory integrals with the form of an ensemble average. The method was developed in 1980s. However, after it was proposed, it had very few applications due to its subtle nature. It is often observed that the CL method converges but the limiting result is incorrect. Less than one decade ago, an improvement of the CL method, called gauge cooling, was proposed, after which the CL method acquired much more attention and was later successfully applied to a number of fields including finite density quantum chromodynamics, superstring theory, and the spin-orbit coupling. In this talk, I will explain the basic idea of the CL method, the reason of its failure, the mechanism and new development of gauge cooling, and the current limitation of the method.

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