Seminars and Colloquia Schedule

Geometric Small Cancellation

Series
Geometry Topology Working Seminar
Time
Monday, August 29, 2016 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shane Scott – Georgia Institute of Technology
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: https://perso.univ-rennes1.fr/vincent.guirardel/papiers/lecture_notes_pc...

Locally integrable non-Liouville analytic geodesic flows on T^2

Series
CDSNS Colloquium
Time
Monday, August 29, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Livia Corsi – Georgia Tech - School of Math
A metric on the 2-torus T^2 is said to be "Liouville" if in some coordinate system it has the form ds^2 = (F(q_1) + G(q_2)) (dq_1^2 + dq_2^2). Let S^*T^2 be the unit cotangent bundle.A "folklore conjecture" states that if a metric is integrable (i.e. the union of invariant 2-dimensional tori form an open and dens set in S^*T^2) then it is Liouville: l will present a counterexample to this conjecture.Precisely I will show that there exists an analytic, non-separable, mechanical Hamiltonian H(p,q) which is integrable on an open subset U of the energy surface {H=1/2}. Moreover I will show that in {H=1/2}\U it is possible to find hyperbolic behavior, which in turn means that there is no analytic first integral on the whole energy surface.This is a work in progress with V. Kaloshin.

Dehn twists exact sequences through Lagrangian cobordism

Series
Geometry Topology Seminar
Time
Monday, August 29, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Weiwei Wu – University of Georgia

In this talk we first introduce a new "singularity-free" approach to the proof of Seidel's long exact sequence, including the fixed-point version. This conveniently generalizes to Dehn twists along Lagrangian submanifolds which are rank one symmetric spaces and their covers, including RPn and CPn, matching a mirror prediction due to Huybrechts and Thomas. The idea of the proof can be interpreted as a "mirror" of the construction in algebraic geometry, realized by a new surgery and cobordism construction. This is a joint work with Cheuk-Yu Mak.

The Beginning of the Year Meeting

Series
Other Talks
Time
Tuesday, August 30, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prasad Tetali – School of Mathematics, Georgia Tech
All School of Mathematics faculty, staff and postdocs are invited to attend this welcome event which will open with a short presentation and introducing new members to the School. Lunch will be provided.

Blowup for model equations of fluid mechanics

Series
PDE Seminar
Time
Tuesday, August 30, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Vu Hoang – Rice University –
The incompressible three-dimensional Euler equations are a basic model of fluid mechanics. Although these equations are more than 200 years old, many fundamental questions remain unanswered, most notably if smooth solutions can form singularities in finite time. In this talk, I discuss recent progress towards proving a finite time blowup for the Euler equations, inspired numerical work by T. Hou and G. Luo and analytical results by A. Kiselev and V. Sverak. My main focus lies on various model equations of fluid mechanics that isolate and capture possible mechanisms for singularity formation. An important theme is to achieve finite-time blowup in a controlled manner using the hyperbolic flow scenario in one and two space dimensions. This talk is based on joint work with B. Orcan-Ekmecki, M. Radosz, and H. Yang.

Two weight estimates with matrix measures for well-localized operators

Series
Analysis Seminar
Time
Wednesday, August 31, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amalia Culiuc – Georgia Tech –
In this talk we discuss two weight estimates for well-localized operators acting on vector-valued function spaces with matrix weights. We will show that the Sawyer-type testing conditions are necessary and sufficient for the boundedness of this class of operators, which includes Haar shifts and their various generalizations. More explicitly, we will show that it is suficient to check the estimates of the operator and its adjoint only on characteristic functions of cubes. This result generalizes the work of Nazarov-Treil-Volberg in the scalar setting and is joint work with K. Bickel, S. Treil, and B. Wick.

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

Link to the Stelson Lecture announcement <a href="http://www.math.gatech.edu/news/stelson-lecture-dr-g-rard-ben-arous" title="http://www.math.gatech.edu/news/stelson-lecture-dr-g-rard-ben-arous">htt...

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.

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.

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.