Seminars and Colloquia by Series

The size of the boundary in the Eden model

Series
Stochastics Seminar
Time
Thursday, September 15, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Damron – School of Mathematics, Georgia Tech
The Eden model, a special case of first-passage percolation, is a stochastic growth model in which an infection that initially occupies the origin of Z^d spreads to neighboring sites at rate 1. Infected sites are colonized permanently; that is, an infected site never heals. It is known that at time t, the infection occupies a set B(t) of vertices with volume of order t^d, and the rescaled set B(t)/t converges to a convex, compact limiting shape. In joint work with J. Hanson and W.-K. Lam, we partially answer a question of K. Burdzy, concerning the order of the size of the boundary of B(t). We show that, in various senses, the boundary is relatively smooth, being typically of order t^{d-1}. This is in contrast to the fractal behavior of interfaces characteristic of percolation models.

Quantitative real algebraic geometry and its applications

Series
School of Mathematics Colloquium
Time
Thursday, September 15, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Saugata Basu – Perdue University
Effective bounds play a very important role in algebraic geometry with many applications. In this talk I will survey recent progress and open questions in the quantitative study ofreal varieties and semi-algebraic sets and their connections with other areas of mathematics -- in particular,connections to incidence geometry via the polynomial partitioning method. I will also discuss some results on the topological complexity of symmetric varieties which have a representation-theoretic flavor. Finally, if time permits I will sketch how some of these results extend to the category of constructible sheaves.

Bloch groups, algebraic K-theory and units

Series
Other Talks
Time
Wednesday, September 14, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Don Zagier – Max Planck Institute for Mathematics Bonn –
We will describe an etale version of Bloch groups and regulators which for the case of number fields that take values in quotients of units of their rings of integers. Joint work with Frank Calegari and Stavros Garoufalidis

A weak type estimate for oscillatory singular integrals

Series
Analysis Seminar
Time
Wednesday, September 14, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Lacey – Georgia Tech
The Ricci-Stein theory of singular integrals concerns operators of the form \int e^{i P(y)} f (x-y) \frac {dy}y.The L^p boundedness was established in the early 1980's, and the weak-type L^1 estimate by Chanillo-Christ in 1987. We establish the weak type estimate for the maximal truncations. This method of proof might well shed much more information about the fine behavior of these transforms. Joint work with Ben Krause.

Homological Stability of Automorphism Groups of Free Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, September 14, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shane Scott – Georgia Tech –
Many algebraic results about free groups can be proven by considering a topological model suggested by Whitehead: glue two handlebodies trivially along their boundary to obtain a closed 3-manifold with free fundamental group. The complex of embedded spheres in the manifold gives a combinatorial model for the automorphism group of the free group. We will discuss how Hatcher uses this complex to show that the homology of the automorphism group is (eventually) independent of the rank of the free group.

Exponential systems over sets with a finite measure

Series
Research Horizons Seminar
Time
Wednesday, September 14, 2016 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Shahaf Nitzan – Department of Mathematics, Georgia Institute of Technology –

Please Note: Food and Drinks will be provided before the seminar.

A fundamental result in Harmonic Analysis states that many functions defined over the interval [-\pi,\pi] can be decomposed into a Fourier series, that is, decomposed as sums of sines and cosines with integer frequencies. This allows one to describe very complicated functions in a simple way, and therefore provides with a strong tool to study the properties of different families of functions.However, the above decomposition does not hold -- or holds but is not efficient enough-- if the functions are no longer defined over an interval,( e.g. if a function is defined over a union of two disjoint intervals). We will discuss the question of whether similar decompositions are possible also in such cases, with the frequencies of the sines and cosines possibly being no longer integers.

Reading group in Nonequilibrium Statistical Mechanics.

Series
Other Talks
Time
Monday, September 12, 2016 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rafel de la Llave – Georgia Tech
The goal of this group is to read carefully the book "Introduction to Chaos in non-equilibrium stat. Mechanics". There will be several speakers. AThe first lecture will be a quick introduction to thermodynamics and statistical mechanics for mathematicians. We hope to explain the physical basis of the problems to mathematicians who have no background in physics and also cover some of the mathematical subtleties that are often overlooked in physiscs courses.

Algorithmic interpretations of fractal dimension

Series
Combinatorics Seminar
Time
Monday, September 12, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Anastasios Sidiropoulos – The Ohio State University
The computational complexity of many geometric problems depends on the dimension of the input space. We study algorithmic problems on spaces of low fractal dimension. There are several well-studied notions of fractal dimension for sets and measures in Euclidean space. We consider a definition of fractal dimension for finite metric spaces, which agrees with standard notions used to empirically estimate the fractal dimension of various sets. When the fractal dimension of the input is lower than the ambient dimension, we obtain faster algorithms for a plethora of classical problems, including TSP, Independent Set, R-Cover, and R-Packing. Interestingly, the dependence of the performance of these algorithms on the fractal dimension closely resembles the currently best-known dependence on the standard Euclidean dimension. For example, our algorithm for TSP has running time 2^O(n^(1-1/delta) * log(n)), on sets of fractal dimension delta; in comparison, the best-known algorithm for sets in d-dimensional Euclidean space has running time 2^O(n^(1-1/d)).

CANCELED Modeling Language Change in Online Social Networks

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 12, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Jacob Eisenstein – GA Tech School of Interactive Computing
Language change is a complex social phenomenon, revealing pathways of communication and sociocultural influence. But while language change has long been a topic of study in sociolinguistics, traditional linguistic research methods rely on circumstantial evidence, estimating the direction of change from differences between older and younger speakers. In this research, we use a data set of several million Twitter users to track language changes in progress. First, we show that language change can be viewed as a form of social influence: we observe complex contagion for ``netspeak'' abbreviations (e.g., lol) and phonetic spellings, but not for older dialect markers from spoken language. Next, we test whether specific types of social network connections are more influential than others, using a parametric Hawkes process model. We find that tie strength plays an important role: densely embedded social ties are significantly better conduits of linguistic influence. Geographic locality appears to play a more limited role: we find relatively little evidence to support the hypothesis that individuals are more influenced by geographically local social ties, even in the usage of geographical dialect markers.

When is a Knot Diagram Legendrian?

Series
Geometry Topology Seminar
Time
Monday, September 12, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mark Lowell – University of Massachusetts
We consider two knot diagrams to be equivalent if they are isotopic without Reidemeister moves, and prove a method for determining if the equivalence class of a knot diagram contains a representative that is the Lagrangian projection of a Legendrian knot. This work gives us a new tool for determining if a Legendrian knot can be de-stabilized.

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