Date/Time : 20 Nov 2020 22:30
Venue : via Zoom
Speaker : Elena Giorgi, Princeton University

https://princeton.zoom.us/j/93296784920 (Joint online mathematical general relativity and hyperbolic PDE seminar) Abstract: The Kerr-Newman spacetime is the most general explicit black hole solution, and represents a stationary rotating charged black hole. Its stability to gravitational and electromagnetic perturbations has eluded a proof since the 80s in the black hole perturbation community, because of “the apparent indissolubility of the coupling between the spin-1 and spin-2 fields in the perturbed spacetime”, as put by Chandrasekhar. We will present a derivation of the Teukolsky and Regge-Wheeler equations in Kerr-Newman in physical space and use it to obtain a quantitative proof of stability

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Date/Time : 19 Nov 2020 09:00
Venue : via Zoom
Speaker : Shen Junliang, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/88455891763?pwd=Sm5ISjNHSnpDVDMzYkFVd2ZBTit2QT09 Meeting ID: 884 5589 1763 Password: 869110 Abstract:  The P=W conjecture by de Cataldo, Hausel, and Migliorini suggests a surprising connection between the topology of Hitchin systems and Hodge theory of character varieties. In this talk, we will focus on interactions between topology of Lagrangian fibrations and Hodge theory in general hyper-Kaehler geometries. Such connections shed new light on both the P=W conjecture for Hitchin systems and the Lagrangian base conjecture for compact hyper-Kähler manifolds.

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Date/Time : 19 Nov 2020 15:00
Venue : via Zoom
Speaker : Haoyang Chen, Fudan University

Join Zoom Meeting https://nus-sg.zoom.us/j/87823796442?pwd=eHBhYmc4Mi9NNlhTczlCdk5neGROQT09 Meeting ID: 87823796442 Password: 132921 Abstract:  In this talk, we generalize a classic result of Lindblad on the scalar quasilinear wave equation and we show that the Cauchy problem for 3D elastic waves, a physical quasilinear wave system with multiple wave-speeds, is ill-posed in $H^3(R^3)$. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. The main difficulties arise from the multiple wave-speeds and its associated non-strict hyperbolicity. We design and combine a geometric approach and an algebraic approach to overcome these difficulties. This is based on joint work with Xinliang An and Silu Yin.

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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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