Date/Time : 08 Dec 2020 16:00
Venue : via Zoom
Speaker : Zhang Shuangjian Kelvin, Ecole Normale Superieure Paris

Join Zoom Meeting https://nus-sg.zoom.us/j/88422472817?pwd=UmFmckRDR2drSVdCZzExR0tGQVVkZz09 Meeting ID: 884 2247 2817 Password: 591367 Abstract:  A monopolist wishes to maximize her profits by finding an optimal price policy. After she announces a menu of products and prices, each agent will choose to buy that product which maximizes his own utility, if positive. The monopolist’s profits are the sum of the net earnings produced by each product sold. These are determined by the costs of production and the distribution of products sold, which in turn are based on the distribution of anonymous agents and the choices they make in response to the monopolist’s price menu. In this talk, I will first review the history of this bi-level maximization problem in microeconomics, including the celebrated work of two Nobel Laureates and one Fields Medalist as well as recent progress on existence, uniqueness, concavity, regularity, and numerical results. When present, concavity makes the problem more amenable to computational and theoretical analysis; it is key to obtaining uniqueness and stability results for the monopolist’s strategy in particular. The beautiful connection to the regularity theory in Optimal Transport will also be addressed. Then I will list a few open problems and discuss some current progress. Part of this talk represents joint work with Professor Robert J. McCann and Professor Guillaume Carlier.

Add to calendar :

Date/Time : 07 Dec 2020 09:00
Venue : via Zoom
Speaker : Kwan Matthew, Stanford University

Join Zoom Meeting https://nus-sg.zoom.us/j/86360904887?pwd=MEFqS1MwcHRTQ0djTHhXUHFFaG43Zz09 Meeting ID: 863 6090 4887 Password: 557853 Abstract: Anti-concentration inequalities provide limits on the extent to which random variables can be concentrated: for example, they commonly give uniform upper bounds on the probability that a random variable takes any particular value. In this talk I’ll discuss some of the many connections between anti-concentration and combinatorics, initially focusing on applications to Ramsey graphs but also touching on a few other topics such as the polynomial Littlewood-Offord problem and permanents of random matrices.

Add to calendar :

Date/Time : 02 Dec 2020 09:00
Venue : via Zoom
Speaker : Yu Zhao, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/85482725152?pwd=em9iM2ZlQk5EZEsyQ3ZIUm9ZVVN3Zz09 Meeting ID: 854 8272 5152 Password: 638381 The quantum toroidal algebra is the affinization of the quantum Heisenberg algebra. Schiffmann-Vasserot, Feigin-Tsymbaliuk and Negut studied the quantum toroidal algebra action on the Grothendieck group of Hilbert schemes of points on surfaces, which generalized the action by Nakajima and Grojnowski in cohomology. In this talk, we will categorify the above quantum toroidal algebra action. Our main technical tool is a detailed geometric study of certain nested Hilbert schemes of triples and quadruples, through the lens of the minimal model program, by showing that these nested Hilbert schemes are either canonical or semi-divisorial log terminal singularities.

Add to calendar :

Date/Time : 01 Dec 2020 09:00
Venue : via Zoom
Speaker : Sun Zheng, Ohio State University

Join Zoom Meeting https://nus-sg.zoom.us/j/87275619715?pwd=WVJrYXVyVVFZbk5meXhna3kycTJEdz09 Meeting ID: 872 7561 9715 Password: 617596 In scientific and engineering computing, we usually encounter numerical discretizations of time-dependent equation systems associated with conserved or decreasing energy. The strong stability of a time stepping method refers to its ability to preserve the monotone energy-decay law at the discrete level, which may provide improved robustness for simulations. In this talk, we present a unified study on strong stability of explicit Runge-Kutta methods for linear semi-negative problems. In particular, we prove a both necessary and sufficient condition for strong stability of arbitrary odd-order methods.

Add to calendar :

Date/Time : 01 Dec 2020 16:00
Venue : via Zoom
Speaker : Filippo Bracci, Rome "Tor Vergata", Italy

Join Zoom Meeting https://nus-sg.zoom.us/j/84662919254?pwd=bXk4WWU2NTFPTEptNkZ3cjBLbGcrZz09 Meeting ID: 846 6291 9254 Password: 206241 Gromov hyperbolic spaces are well studied since their introduction. In 2000 Balogh and Bonk proved that bounded strongly pseudoconvex domains are Gromov hyperbolic with respect to the Kobayashi distance and the natural boundary is homeomorphic to the Gromov boundary. It was however only in the last five years that Gromov hyperbolicity was started to be used in depth in complex analysis. The most useful tool in Gromov hyperbolicity is the so-called “shadowing lemma”. In this talk I will present a general introduction to Gromov hyperbolicity in complex analysis and review some recent results and applications to one and several complex variables (such as the study of trajectory of semi-complete holomorphic vector fields in the unit disc and boundary extension results for biholomorphisms in scv without assuming boundary regularity of the domains).

Add to calendar :

Date/Time : 25 Nov 2020 09:00
Venue : via Zoom
Speaker : Tong Jiajun, University of California, Los Angeles

Join Zoom Meeting https://nus-sg.zoom.us/j/87962970385?pwd=QnRENCtzSW55VXArejBpWUtXcmlyUT09 Meeting ID: 879 6297 0385 Password: 808752 Abstract:  We study a two-phase tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues into the exterior vacuum. Instead of considering evolution of cell densities, our focus will be on the dynamics of two moving interfaces in the model that separate the tumor, the normal tissue, and the exterior vacuum. We will discuss well-posedness results on the interface evolution starting from a nearly radial initial configuration, under the assumption that the tumor has lower mobility than the normal tissue, which is in line with the well-known Saffman-Taylor condition in viscous fingering. We will briefly discuss possible ill-posedness scenarios when these conditions are violated, as well as implications of our results on further analysis of the tumor growth models. This is joint work with Inwon Kim.

Add to calendar :

Date/Time : 23 Nov 2020 09:00
Venue : via Zoom
Speaker : Yao Yao, Georgia Institute of Technology

Join Zoom Meeting https://nus-sg.zoom.us/j/81762064402?pwd=Z250ZmtKTFVhUDNqTzFlN0pvdldoQT09 Meeting ID: 817 6206 4402 Password: 845588 Abstract:  For any nonnegative density f and radially decreasing interaction potential W, the celebrated Riesz rearrangement inequality shows the interaction energy E[f] = \int f(x)f(y)W(x-y) dxdy satisfies E[f] <= E[f^*], where f^* is the radially decreasing rearrangement of f. It is a natural question to look for a quantitative version of this inequality: if its two sides almost agree, how close must f be to a translation of f^*? Previously the stability estimate was only known for characteristic functions. I will talk about a recent work with Xukai Yan, where we found a simple proof of stability estimates for general densities. I will also discuss its connection with some nonlocal PDEs such as the aggregation-diffusion equation.

Add to calendar :

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

Add to calendar :

Date/Time : 20 Nov 2020 09:00
Venue : via Zoom
Speaker : Xiaochuan Tian, University of California, San Diego

Join Zoom Meeting Meeting ID: 879 3214 5555 Password: 996723 Abstract: Nonlocal continuum models are in general integro-differential equations in place of the conventional partial differential equations.  While nonlocal models show their effectiveness in modeling a number of anomalous and singular processes in physics and material sciences, for example, the peridynamics model of fracture mechanics, they also come with increased difficulty in computation with nonlocality involved.  We present in this talk numerical methods for nonlocal models characterized by a length parameter which measures the range of nonlocal interactions.  Several numerical methods will be discussed with a focus on asymptotic compatibility of the schemes that are robust under the change of the nonlocal length parameter.

Add to calendar :