May 2015
Graduate Student Geometric Analysis Seminar
Speaker: Kyeongsu Choi Title: "The uniqueness of complete convex solutions to the mean curvature flow" Ref: K. Ecker & G. Huisken
Find out more »Informal Mathematical Physics Seminar
Speaker: Dmitry Galakhov Title: "Spectral Networks with Spin" Abstract: The spectral network technique give a nice approach to a study of Donaldson-Thomas invariants of Calabi-Yau threefolds and homological theory of semi-stable quiver representations via behavior of certain differential equation solutions. These theories are known to perform a wall-crossing phenomena when the invariants start to change discontinuously in the space of stability parameters across certain co-dimension 1 surfaces. We refine combinatorics of spetral networks with an extra grading to get so…
Find out more »COLUMBIA PROBABILITY SEMINAR
Speaker: Claudio Landim (IMPA Rio de Janeiro) Title: "Condensing zero-range processes" Abstract: Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. Consider a condensing zero-range process with $N$ particles evolving on a fixed and finite set $S$. In the diffusive time scale $N^2$ the fraction of particles at each site evolves as a diffusion whose drift is unbounded. The process…
Find out more »Columbia Geometry & Analysis Seminar
Speaker:Matteo Bonforte, (Univesidad Autonoma de Madrid) Title: "A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on bounded domains" Abstract: We investigate quantitative properties of nonnegative solutions u(t, x) ≥ 0 to the nonlinear fractional diffusion equation, ∂tu + L(um) = 0, posed in a boundeddomain,x∈Ω⊂RN fort>0andm>1. AsLwecantake the most common definitions of the fractional Laplacian (−∆)s, 0 < s < 1, in a bounded domain with zero Dirichlet boundary conditions, as well as more general classes of operators. We consider…
Find out more »Perspectives on Complex Algebraic Geometry
This workshop, to be held at Columbia from May 22 to May 25, celebrates the achievements and influence of Robert Friedman on the occasion of his 60th birthday. It will focus on the topology and geometry of algebraic surfaces and 4-manifolds, vector bundles and G-bundles, and geometric applications of Hodge theory. Further information, with a list of speakers and talks, may be found at: https://sites.google.com/site/complexalgebraicgeometry/home
Find out more »June 2015
Geometric Analysis Seminar
Speaker: Paul Bryan (UC San Diego) Title: "Weak differential inequalities for the Isoperimetric profile and comparison results." Abstract: The isoperimetric profile of a Riemannian manifold gives the least perimeter for a given fixed volume. Using variation techniques, a weak differential inequality may be obtained for the profile. I will describe how this inequality may then be used to obtain comparison results such as the Levy-Gromov isoperimetric inequality. As a geometric functional, the profile is influenced by curvature and topology. I…
Find out more »Geometric Analysis Seminar
Speaker: Or Hershkovits (NYU Courant) Title: "Mean Curvature Flow of Reifenberg Sets." Abstract: The mean curvature flow, the gradient flow of the area functional, is one of the most natural geometric flows to consider for embedded hyper-surfaces in R^{n+1}. Classically, given a sufficiently smooth hyper-surface (for which both the area and its gradient are defined), there exists a unique flow starting from it that exists for some positive time. Moreover, the flow smooths the hyper-surface instantaneously. In the early 90s it…
Find out more »Geometric Analysis Seminar
Speaker: Paul Bryan (UC San Diego) Title: "Weak differential inequalities for the Isoperimetric profile and comparison results, Part II" Abstract: The isoperimetric profile of a Riemannian manifold gives the least perimeter for a given fixed volume. Using variation techniques, a weak differential inequality may be obtained for the profile. I will describe how this inequality may then be used to obtain comparison results such as the Levy-Gromov isoperimetric inequality. As a geometric functional, the profile is influenced by curvature and topology.…
Find out more »January 2016
2016 SPRING TERM LECTURE SERIES
Sergiu Klainerman (Columbia University and Princeton University) “INTRODUCTION TO THE MATHEMATICAL THEORY OF BLACK HOLES” This is meant to be an introduction to the beautiful mathematical theory of Black Holes. The audience is expected to have some familiarity with the basic concepts in Riemannian Geometry and the basic properties of differential equations, such as the local existence result for ODE’s and the elementary properties of the standard Laplace, Heat and Wave equations (as exposed, for example, in the PDE books of…
Find out more »March 2017
Schramm-Loewner Evolutions, Gaussian Free Field and Liouville Quantum Gravity
A workshop at Columbia University, March 13 - 17, 2017 The meeting is centered around recent advances in Schramm-Loewner Evolutions, Gaussian Free Field and Liouville Quantum Gravity. Organizers: Julien Dubedat (Columbia), Fredrik Viklund (KTH). The workshop is supported by the National Science Foundation (DMS 1308476) For more information please visit: SLE, GFF AND LQG in NYC
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