Date/Time : 10 Oct 2023 10:30
Venue : S17 #04-06 (SR1)
Speaker : Charles Cheung, NVIDIA AI Technology Center

In this talk, I will talk about a few directions and use cases of AI for Science. PINNs and neural operator are used for solving many engineering problems that involves differential equations. We will walk through the basic concept of PINNs and neural operator and introduce NVIDIA modulus, an SDK for training PINNs and neural operator. We will also share a recent project about transfer learning.

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Date/Time : 06 Oct 2023 15:00
Venue : S17 #05-11 (SR5)
Speaker : Gordan Savin, University of Utah

I will review basic definitions of Fell topology and results of Milicic and Tadic, then discuss several results and problems involving the Fell topology on unitary generic representations:
Does a sequence of unitary generic representations contains a generic representation as a cluster point? Is a generic discrete series isolated in the unitary dual?

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Date/Time : 06 Oct 2023 16:30
Venue : S17 #05-11 (SR5)
Speaker : Bryan Wang Peng Jun, National University of Singapore

Recent work of Ben-Zvi, Sakellaridis and Venkatesh (BZSV) predicts the existence of a duality in the relative Langlands program, indexed by a class of Hamiltonian spaces with reductive group action. I will first give a rough introduction to the BZSV-duality, focusing on motivations and a series of motivating examples. Then, I will explain a local incarnation of the BZSV-duality in the setting of branching problems, and how the generalised Whittaker (or Gelfand-Graev) models serve as the prototypical example. Finally, I will present a new family of examples of BZSV-duality, which can so far be verified in this local setting. Time permitting, I will explain the proof, which proceeds via results of Gomez and Zhu, and an interesting interpretation in the framework of Hamiltonian spaces. This is based on my thesis work supervised by Wee Teck Gan.

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Date/Time : 05 Oct 2023 15:30
Venue : S17 #04-06 (SR1)
Speaker : Zhe Sun, University of Science and Technology of China

Fock and Goncharov introduced a pair of mirror moduli spaces associated to G and G^L which generalized the Teichmüller space and the decorated Teichmüller space, and they proposed a duality: the canonical basis of the regular function ring of one space X is parameterized by the tropical integral points of its mirror X^V. In this talk, I will explain my joint work with Linhui Shen and Daping Weng for SL3, where we introduce the topological asymmetric intersection numbers between webs on the surfaces to provide the duality pairings and the map from webs to tropical points. We prove that the map is the same as the previous one obtained by Douglas and myself. We relate the cluster algebra and skein algebra by this intersection number and prove the mutation equivariance, where the flip equivariance is a consequence.

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Date/Time : 04 Oct 2023 14:30
Venue : S17 #05-11 (SR5)
Speaker : Shiwu Yang, Peking University

It has been shown that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space decay like linear solutions. One hence can define the associated radiation field on the future null infinity. In this talk, we show the existence of a global solution to the MKG system which scatters to any given sufficiently localized radiation field with arbitrarily large size and total charge. The result follows by studying the characteristic initial value problem to the MKG system with general large data by using gauge invariant vector field method. This is based on joint work with W. Dai, H. Mei and D. Wei.

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Date/Time : 04 Oct 2023 13:00
Venue : via Zoom
Speaker : Shengtong Zhang, Stanford University

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

Meeting ID: 810 4646 2775
Passcode: 23571113

In this talk, we start with Nikiforov’s spectral version of Turan’s theorem. This leads us to an intriguing conjecture of Bollobas and Nikiforov on the first two eigenvalues of graphs. Despite its simple appearance, the conjecture has resisted attacks for over 15 years. We survey several partial results on this conjecture, up to some recent progress by the speaker confirming the conjecture in the case of regular graphs. Based on https://arxiv.org/abs/2309.08184.

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Date/Time : 04 Oct 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Wilderich Tuschmann, Karlsruhe Institute of Technology

Consider a smooth manifold with a Riemannian metric satisfying some sort of geometric constraint like, for example, positive scalar curvature, non-negative Ricci or negative sectional curvature, being Einstein, Kähler, Sasakian, etc. A natural question to ponder is then what the space of all such metrics does look like. Moreover, one can also study this question for the corresponding moduli spaces of metrics, i.e., quotients of the former by the diffeomorphism group of the manifold, acting by pulling back metrics. These spaces are customarily equipped with the topology of smooth convergence on compact subsets and the quotient topology, respectively, and their topological properties then provide the right means to measure ‘how many’ different metrics and geometries the given manifold actually does exhibit.

In my talk, I will provide a short introduction to the subject with a focus on lower curvature bounds and then discuss non-traditional approaches to these objects via Gromov-Hausdorff convergence techniques which, in particular, also allow for the study of natural compactifications. Moreover, I will describe the moduli spaces of flat metrics on closed manifolds in a new way via symmetric spaces and, if time permits, also discuss some potential applications arising from this.

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Date/Time : 21 Sep 2023 15:30
Venue : S17 #04-06 (SR1)
Speaker : Tan Ser Peow, National University of Singapore

The congruence subgroup Gamma_0(N) is the subgroup of the modular group PSL(2,Z) where the lower left-hand entry is congruent to 0 mod N. By a theorem of Kurosh, since PSL(2,Z) is freely generated by an element of order 2 and an element of order 3, any finite index subgroup of PSL(2,Z) can be freely generated by elements of order 2,3 and infinity, including Gamma_0(N).

Kulkarni used an algebraic-geometric method to give an algorithm for finding these generators, and he observed that when N is a prime less than 100, these generators can be chosen so that the lower left-hand entry is either N or 0. He conjectured that this is true for all primes. We call such a generating set an optimal generating system and we will discuss in this talk how to prove Kulkarni’s conjecture, with extensions to cases where N is the square of a prime. This is joint work with Nhat Minh Doan, Sanghyun Kim and Mong Lung Lang.

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Date/Time : 20 Sep 2023 15:00
Venue : S16 #04-35
Speaker : Goh Jun Le, National University of Singapore

We apply and reframe statements about graph decompositions, Latin squares, affine planes, etc. to statements about reductions between problems. In particular, we exhibit a statement (depending on n) which is equivalent to the existence of a finite affine plane of order n (open for many n). I expect this talk to be accessible to undergraduates.

Joint work with David Belanger and Damir Dzhafarov.

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