Seminars and Colloquia by Series

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.

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.

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.

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

Please Note: 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.

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.

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...

The phase transition in the random d-process

Series
Combinatorics Seminar
Time
Friday, August 26, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lutz Warnke – Georgia Tech
One of the most interesting features of Erdös-Rényi random graphs is the `percolation phase transition', where the global structure intuitively changes from only small components to a single giant component plus small ones. In this talk we discuss the percolation phase transition in the random d-process, which corresponds to a natural algorithmic model for generating random regular graphs (starting with an empty graph on n vertices, it evolves by sequentially adding new random edges so that the maximum degree remains at most d). Our results on the phase transition solve a problem of Wormald from 1997, and verify a conjecture of Balinska and Quintas from 1990. Based on joint work with Nick Wormald (Monash University).

Lifting Homeomorphisms of Cyclic Branched Covers of Spheres

Series
Geometry Topology Seminar
Time
Monday, August 22, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rebecca Winarski – University of Wisconsin at Milwaukee
Birman and Hilden ask: given finite branched cover X over the 2-sphere, does every homeomorphism of the sphere lift to a homeomorphism of X? For covers of degree 2, the answer is yes, but the answer is sometimes yes and sometimes no for higher degree covers. In joint work with Ghaswala, we completely answer the question for cyclic branched covers. When the answer is yes, there is an embedding of the mapping class group of the sphere into a finite quotient of the mapping class group of X. In a family where the answer is no, we find a presentation for the group of isotopy classes of homeomorphisms of the sphere that do lift, which is a finite index subgroup of the mapping class group of the sphere. Our family introduces new examples of orbifold Picard groups of subloci of Teichmuller space that are finitely generated but not cyclic.

GT MAP Workshop on Materials

Series
GT-MAP Seminar
Time
Wednesday, August 17, 2016 - 09:30 for 8 hours (full day)
Location
Skiles 249
Speaker
Various speakers – Georgia Tech
The workshop will launch the themetic semester on Material for GT-MAP activities. This is a three day workshop: The first two days (Wed, Thurs) focusing on the theme of Material, and third day includes broad research topics, open to introducing your research. See the complete Schedule.

Difference of convex functions for eigenvalue problems

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 8, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Yunho Kim – UNIST, Korea
Inspired by the usefulness of difference of convex functions in some problems, e.g. sparse representations, we use such an idea of difference of convex functions to propose a method of finding an eigenfunction of a self-adjointoperator. In a matrix setting, this method always finds an eigenvector of a symmetric matrix corresponding to the smallest eigenvalue without solving Ax=b. In fact, such a matrix A is allowed to be singular, as well. We can apply the same setting to a generalized eigenvalue problem. We will discuss its convergence as well.

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