Seminars and Colloquia by Series

Geometric Small Cancellation

Series
Geometry Topology Working Seminar
Time
Monday, September 12, 2016 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Justin Lanier – Georgia Tech
In this lecture series, held jointly (via video conference) with the University of Buffalo and the University of Arkansas, we aim to understand the lecture notes by Vincent Guirardel on geometric small cancellation. The lecture notes can be found here: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pcmi.pdf This week we will finish the section on rotating families (Lecture 3).

Counting Independent Sets in Regular Hypergraphs

Series
Combinatorics Seminar
Time
Friday, September 9, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Emma Cohen – Georgia Tech

Please Note: Joint work with Will Perkins and Prasad Tetali.

We consider the extremal counting problem which asks what d-regular, r-uniform hypergraph on n vertices has the largest number of (strong) independent sets. Our goal is to generalize known results for number of matchings and independent sets in regular graphs to give a general bound in the hypergraph case. In particular, we propose an adaptation to the hypergraph setting of the occupancy fraction method pioneered by Davies et al. (2016) for use in the case of graph matchings. Analysis of the resulting LP leads to a new bound for the case r=3 and suggests a method for tackling the general case.

Models for Mapping Class Groups II

Series
Geometry Topology Working Seminar
Time
Friday, September 9, 2016 - 14:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Institute of Technology
A celebrated theorem of Nikolai Ivanov states that the automorphism group of the mapping class group is again the mapping class group. The key ingredient is his theorem that the automorphism group of the complex of curves is the mapping class group. After many similar results were proved, Ivanov made a metaconjecture that any “sufficiently rich object” associated to a surface should have automorphism group the mapping class group. In joint work with Tara Brendle, we show that the typical normal subgroup of the mapping class group (with commuting elements) has automorphism group the mapping class group. To do this, we show that a very large family of complexes associated to a surface has automorphism group the mapping class group.

The invariable Ewens distribution

Series
Stochastics Seminar
Time
Thursday, September 8, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Matthew Junge – Duke University –
Form a multiset by including Poisson(1/k) copies of each positive integer k, and consider the sumset---the set of all finite sums from the Poisson multiset. It was shown recently that four such (independent) sumsets have a finite intersection, while three have infinitely many common elements. Uncoincidentally, four uniformly random permutations will invariably generate S_n with asymptotically positive probability, while three will not. What is so special about four? Not much. We show that this result is a special case of the "ubiqituous" Ewens sampling formula. By varying the distribution's parameter we can vary the number of random permutations needed to invariably generate S_n, and, relatedly, the number of Poisson sumsets to have finite intersection. *Joint with Gerandy Brita Montes de Oca, Christopher Fowler, and Avi Levy.

L^p Estimates for Semi-Degenerate Simplex Multipliers

Series
Analysis Seminar
Time
Wednesday, September 7, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Kesler – Georgia Tech
Multilinear singular integral operators associated to simplexes arise naturally in the dynamics of AKNS systems. One area of research has been to understand how the choice of simplex affects the estimates for the corresponding operator. In particular, C. Muscalu, T. Tao, C. Thiele have observed that degenerate simplexes yield operators satisfying no L^p estimates, while non-degenerate simplex operators, e.g. the trilinear Biest, satisfy a wide range of L^p estimates provable using time-frequency arguments. In this talk, we shall define so-called semi-degenerate simplex multipliers, which as the terminology suggests, lie somewhere between the degenerate and non-degenerate settings and then introduce new L^p estimates for such objects. These results are known to be sharp with respect to target Lebesgue exponents, unlike the best known Biest estimates, and rely on carefully localized interpolation arguments

Geometric Small Cancellation

Series
Geometry Topology Working Seminar
Time
Tuesday, September 6, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Justin Lanier – Georgia Tech
In this lecture series, held jointly (via video conference) with the University of Buffalo and the University of Arkansas, we aim to understand the lecture notes by Vincent Guirardel on geometric small cancellation. The lecture notes can be found here: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pcmi.pdf

Models for Mapping Class Groups I

Series
Geometry Topology Working Seminar
Time
Friday, September 2, 2016 - 14:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 256
Speaker
Dan Margalit – Georgia Institute of Technology
A celebrated theorem of Nikolai Ivanov states that the automorphism group of the mapping class group is again the mapping class group. The key ingredient is his theorem that the automorphism group of the complex of curves is the mapping class group. After many similar results were proved, Ivanov made a metaconjecture that any “sufficiently rich object” associated to a surface should have automorphism group the mapping class group. In joint work with Tara Brendle, we show that the typical normal subgroup of the mapping class group (with commuting elements) has automorphism group the mapping class group. To do this, we show that a very large family of complexes associated to a surface has automorphism group the mapping class group.

Special TK_5 in graphs containing K_4^-

Series
Dissertation Defense
Time
Friday, September 2, 2016 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Dawei He – School of Mathematics, Georgia Tech
The well-known Kelmans-Seymour conjecture states that every nonplanar 5-connected graph contains TK_5. Ma and Yu prove the conjecture for graphs containing K_4^- . In the thesis, we will find special TK_5 in graphs containing K_4^-, i.e. two versions of generalization of their result will be dealt with separately.

The Complexity of Random Functions of Many Variables II

Series
School of Mathematics Colloquium
Time
Thursday, September 1, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gérard Ben Arous – Courant Institute, NYU

Please Note: Link to the Stelson Lecture announcement http://www.math.gatech.edu/news/stelson-lecture-dr-g-rard-ben-arous

This Colloquium will be Part II of the Stelson Lecture. A function of many variables, when chosen at random, is typically very complex. It has an exponentially large number of local minima or maxima, or critical points. It defines a very complex landscape, the topology of its level lines (for instance their Euler characteristic) is surprisingly complex. This complex picture is valid even in very simple cases, for random homogeneous polynomials of degree p larger than 2. This has important consequences. For instance trying to find the minimum value of such a function may thus be very difficult. The mathematical tool suited to understand this complexity is the spectral theory of large random matrices. The classification of the different types of complexity has been understood for a few decades in the statistical physics of disordered media, and in particular spin-glasses, where the random functions may define the energy landscapes. It is also relevant in many other fields, including computer science and Machine learning. I will review recent work with collaborators in mathematics (A. Auffinger, J. Cerny) , statistical physics (C. Cammarota, G. Biroli, Y. Fyodorov, B. Khoruzenko), and computer science (Y. LeCun and his team at Facebook, A. Choromanska, L. Sagun among others), as well as recent work of E. Subag and E.Subag and O.Zeitouni.

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