Seminars and Colloquia by Series

Almost-reducibility for fibered holomorphic dynamics

Series
Dynamical Systems Working Seminar
Time
Tuesday, November 17, 2015 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mikel Viana – Georgia Tech (Math)
In previous talks, we discussed an algorithm (Nash-Moser iteration) to compute invariant whiskered tori for fibered holomorphic maps. Several geometric and number-theoretic conditions are necessary to carry out each step of the iteration. Recently, there has been interest in studying what happens if some of the conditions are removed. In particular, the second Melnikov condition we found can be hard to verify in higher dimensional problems. In this talk, we will use a method due to Eliasson, Moser and Poschel to obtain quasi-periodic solutions which, however, lose an important geometric property relative to the solutions previously constructed.

Uniqueness and Finsler type optimal transport metric for nonlinear wave equations

Series
PDE Seminar
Time
Tuesday, November 17, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Geng Chen – School of Mathematics, Georgia Tech
In this talk, we will discuss a sequence of recent progresses on the global well-posedness of energy conservative Holder continuous weak solutions for a class of nonlinear variational wave equations and the Camassa-Holm equation, etc. A typical feature of solutions in these equations is the formation of cusp singularity and peaked soliton waves (peakons), even when initial data are smooth. The lack of Lipschitz continuity of solutions gives the major difficulty in studying the well-posedness and behaviors of solutions. Several collaboration works with Alberto Bressan will be discussed, including the uniqueness by characteristic method, Lipschitz continuous dependence on a Finsler type optimal transport metric and a generic regularity result using Thom's transversality theorem.

Random graph processes with dependencies

Series
Job Candidate Talk
Time
Tuesday, November 17, 2015 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Lutz Warnke – University of Cambridge
Random graphs are the basic mathematical models for large-scale disordered networks in many different fields (e.g., physics, biology, sociology). Their systematic study was pioneered by Erdoes and Renyi around 1960, and one key feature of many classical models is that the edges appear independently. While this makes them amenable to a rigorous analysis, it is desirable (both mathematically and in terms of applications) to understand more complicated situations. In this talk I will discuss some of my work on so-called Achlioptas processes, which (i) are evolving random graph models with dependencies between the edges and (ii) give rise to more interesting percolation phase transition phenomena than the classical Erdoes-Renyi model.

Topological full groups

Series
Colloquia
Time
Tuesday, November 17, 2015 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Volodymyr Nekrashevych – Department of Mathematics, Texas A&M –

Please Note: This talk should interest people in Algebra, Dynamical Systems and Mathematical Physics in addition to Geometry and Topology. Volodia Nekrashevych will visit Atlanta from Sunday November 15th evening until Tuesday November 17th afternoon. He will be available for private talks on Monday November 14th after noon or on Tueasday morning before 10AM. Contact him directly by email or contact jeanbel@math.gatech.edu to schedule a meeting or to have a dinner with him.

Topological full groups are naturally associated with semigroups of local homeomorphisms: iterations of a single homeomorphism, holonomy groupoids of laminations, groupoids of local isomorphisms of quasiperiodic sets (for example Penrose tilings), etc. Some of these groups have interesting properties from the point of view of group theory. For instance, they provide first examples of amenable infinite simple finitely generated groups (by a result of K. Juschenko and N. Monod) and first examples of simple amenable groups of Burnside type. The full group of the Penrose tiling is another interesting example from the point of view of amenability.

Secants of the Veronese and the Determinant

Series
Algebra Seminar
Time
Monday, November 16, 2015 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cameron Farnsworth – Texas A&M –
Let det_n be the homogeneous polynomial obtained by taking the determinant of an n x n matrix of indeterminates. In this presentation linear maps called Young flattenings will be defined and will be used to show new lower bounds on the symmetric border rank of det_n.

Stochastic models of collective motion

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 16, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gil Ariel – Bar-Ilan University
Collective movement is one of the most prevailing observations in nature. Yet, despite considerable progress, many of the theoretical principles underlying the emergence of large scale synchronization among moving individuals are still poorly understood. For example, a key question in the study of animal motion is how the details of locomotion, interaction between individuals and the environment contribute to the macroscopic dynamics of the hoard, flock or swarm. The talk will present some of the prevailing models for swarming and collective motion with emphasis on stochastic descriptions. The goal is to identify some generic characteristics regarding the build-up and maintenance of collective order in swarms. In particular, whether order and disorder correspond to different phases, requiring external environmental changes to induce a transition, or rather meta-stable states of the dynamics, suggesting that the emergence of order is kinetic. Different aspects of the phenomenon will be presented, from experiments with locusts to our own attempts towards a statistical physics of collective motion.

Trisecting Smooth 4-manifolds with Boundary

Series
Geometry Topology Seminar
Time
Monday, November 16, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nick Castro – University of Georgia
A trisection of a smooth, oriented, compact 4-manifold X is a decomposition into three diffeomorphic 4-dimensional 1-handlebodies with certain nice intersections properties. This is a very natural 4-dimensional analog of Heegaard splittings of 3-manifolds. In this talk I will define trisections of closed 4-manifolds, but will quickly move to the case of 4-manifolds with connected boundary. I will discuss how these "relative trisections" interact with open book decompositions on the bounding 3-manifold. Finally, I will discuss a gluing theorem which allows us to glue together relative trisections to induce a trisection on a closed 4-manifold.

Effective equidistribution of horocycle maps

Series
CDSNS Colloquium
Time
Monday, November 16, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James Tanis – College de France
We prove results concerning the equidistribution of some "sparse" subsets of orbits of horocycle flows on $SL(2, R)$ mod lattice. As a consequence of our analysis, we recover the best known rate of growth of Fourier coefficients of cusp forms for arbitrary noncompact lattices of $SL(2, R)$, up to a logarithmic factor. This talk addresses joint work with Livio Flaminio, Giovanni Forni and Pankaj Vishe.

ALS - Coloring and girth

Series
Other Talks
Time
Sunday, November 15, 2015 - 09:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Noga Alon – Tel Aviv University and IAS, Princeton

Please Note: Second featured lecture in the Atlanta Lecture Series in Combinatorics and Graph Theory mini-conference

The study of graphs with high girth and high chromatic number had a profound influence on the history of Combinatrics and Graph Theory, and led to the development of sophisticated methods involving tools from probability, topology, number theory, algebra and combinatorics. I will discuss the topic focusing on a recent new explicit construction of graphs (and hypergraphs) of high girth and high chromatic number, in joint work with Kostochka, Reiniger, West and Zhu.

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