Thursday January 25, 2018 4:00 PM  5:00 PM Math Tower P131
 Frank Thorne, University of South Carolina
An Analytic View of Arithmetic Statistics"Arithmetic statistics" is all about counting arithmetic objects: number fields, ideal class groups, Selmer groups of ellitpic curves, and so on. One common approach is to parametrize such objects in terms of lattice points in a vector space, up to an equivalence relation given by the action of a suitable group. One then counts the lattice points.
I will give an overview of some work on this subject, from Gauss to contemporary work of Manjul Bhargava, myself, my host Bob Hough, and many others. I will concentrate on the analytic and quantitative side of the subject, and explain how refinements to our lattice point counting methods lead to improved results.

Thursday February 01, 2018 4:00 PM  5:00 PM Math Tower P131
 Xiuxiong Chen, Stony Brook University
On constant scalar curvature Kaehler metricsInspired by the celebrated $C^0, C^2 $ and $C^3$ a priori estimates of Calabi, Yau and others on Kaehler Einstein metrics, we present a report on a priori estimates on constant scalar curvature Kaehler metrics. With this estimate, we prove the Donaldson conjecture on geodesic stability and the well known properness conjecture on the Mabuchi energy functional. This is a joint work with Cheng JingRui from University of Wisconsin at Madison.
This lecture is intended to be expository. This will be followed by a more
technical lecture by Dr. Cheng Jingrui on Geometry/topology seminar (Feb. 6th).

Thursday February 15, 2018 4:00 PM  5:00 PM Math Tower P131
 Leonid Kovalev, Syracuse University
Lipschitz geometry of finite subset spacesLet $X(n)$ be the set of all nonempty subsets of a metric space X with cardinality at most n. Equipped with the Hausdorff metric, $X(n)$ becomes a metric space of its own, a finite subset space of X. Such spaces have been studied since the 1931 paper of Borsuk and Ulam, mostly from the topological perspective. The investigation of their metric structure is more recent.
The finite subset spaces form a natural chain of isometric embeddings: $X = X(1) ⊂ X(2) ⊂ X(3) ⊂ ...$ For example, when X is a circle, this chain describes a trefoil knot bounding a Möbius strip in the 3sphere. For some classes of spaces these embedding split, even in the Lipschitz category. The existence of Lipschitz retractions $X(n) → X(n1)$ generally corresponds to X being nonpositively curved, but the exact relationship is yet to be understood.

Thursday February 22, 2018 4:00 PM  5:00 PM Math Tower P131
 Nets Katz, Caltech
Semialgebraic sets and the Kakeya ProblemIn joint work with Keith Rogers, we study the connection between the Kakeya problem and the highlights of the theory of semialgebraic sets such as Tarski's projection theorem and Gromov's algebraic lemma.

Thursday March 01, 2018 4:00 PM  5:00 PM Math Tower P131
 Dzmitry Dudko,
On the problem of local connectivity of the Mandelbrot set.The Mandelbrot set encodes how the dynamics of $z^2+c$ depends on $c$. In the 1980s A. Douady and J. Hubbard conjectured that the Mandelbrot set is locally connected  the MLC conjecture. This conjecture would result in a simple abstract ``pinched disk'' model for the Mandelbrot set. Since the 1990s, local connectivity was established for a large class of parameters, but the full conjecture is still open. In the talk we will discuss recent developments in the area. Our main tool is ``Pacman renormalization'' responsible for selfsimilarity of the Mandelbrot set near its main cardioid.
Based on a joint work with Misha Lyubich.

Thursday March 08, 2018 4:00 PM  5:00 PM Math Tower P131
 Richard Melrose, MIT
TBATBA

Thursday April 12, 2018 4:00 PM  5:00 PM SCGP102
 TBA, TBA
Categorification in mathematical physics workshop ColloquiumTBA

Thursday April 19, 2018 4:00 PM  5:00 PM Math Tower P131
 Percy Deift, NYU Courant
TBATBA

Thursday April 26, 2018 4:00 PM  5:00 PM Math Tower P131
 Mohammed Abouzaid, Columbia University
TBATBA

