Seminars and Colloquia by Series

Singularity formation in Compressible Euler equations (Part IV)

Series
PDE Working Seminar
Time
Thursday, November 20, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ronghua Pan – GeorgiaTech –
Compressible Euler equations describe the motion of compressible inviscid fluid. Physically, it states the basic conservation laws of mass, momentum, and energy. As one of the most important examples of nonlinear hyperbolic conservation laws, it is well-known that singularity will form in the solutions of Compressible Euler equations even with small smooth initial data. This talk will discuss some classical results in this direction, including some most recent results for the problem with large initial data.

Effective Chabauty for symmetric powers of curves

Series
Algebra Seminar
Time
Wednesday, November 19, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Park – McGill University
Faltings' theorem states that curves of genus g> 1 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the number of rational points, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed that Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of the curve is smaller than g, can be used to give a good effective bound on the number of rational points of curves of genus g > 1. We draw ideas from nonarchimedean geometry and tropical geometry to show that we can also give an effective bound on the number of rational points outside of the special set of the d-th symmetric power of X, where X is a curve of genus g > d, when the Mordell-Weil rank of the Jacobian of the curve is at most g-d.

Mutliparameter singular integrals

Series
Analysis Seminar
Time
Wednesday, November 19, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Brian Street – University of Wisconsin, Madison
This talk concerns a theory of "multiparameter singularintegrals." The Calderon-Zygmund theory of singular integrals is a welldeveloped and general theory of singular integrals--in it, singularintegrals are associated to an underlying family of "balls" B(x,r) on theambient space. We talk about generalizations where these balls depend onmore than one "radius" parameter B(x,r_1,r_2,\ldots, r_k). Thesegeneralizations contain the classical "product theory" of singularintegrals as well as the well-studied "flag kernels," but also include moregeneral examples. Depending on the assumptions one places on the balls,different aspects of the Calderon-Zygmund theory generalize.

Dehn-Nielsen-Baer Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 19, 2014 - 02:01 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Elizabeth Bolduc – Georgia Tech
The Dehn Nielsen Baer Theorem states that the extended mapping class group is isomorphic to the outer automorphisms of π1(Sg). The theorem highlights the connection between the topological invariant of distinct symmetries of a space and its fundamental group. This talk will incorporate ideas from algebra, topology, and hyperbolic geometry!

On the geometry of log concave measures

Series
Job Candidate Talk
Time
Tuesday, November 18, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Galyna Livshyts – Kent State University
The perimeter of a convex set in R^n with respect to a given measure is the measure's density averaged against the surface measure of the set. It was proved by Ball in 1993 that the perimeter of a convex set in R^n with respect to the standard Gaussian measure is asymptotically bounded from above by n^{1/4}. Nazarov in 2003 showed the sharpness of this bound. We are going to discuss the question of maximizing the perimeter of a convex set in R^n with respect to any log-concave rotation invariant probability measure. The latter asymptotic maximum is expressed in terms of the measure's natural parameters: the expectation and the variance of the absolute value of the random vector distributed with respect to the measure. We are also going to discuss some related questions on the geometry and isoperimetric properties of log-concave measures.

The Talbot effect in a non-linear dynamics.

Series
School of Mathematics Colloquium
Time
Tuesday, November 18, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Luis Vega – BCAM-Basque Center for Applied Mathematics (Scientific Director) and University of the Basque Country UPV/EHU –
In the first part of the talk I shall present a linear model based on the Schrodinger equation with constant coefficient and periodic boundary conditions that explains the so-called Talbot effect in optics. In the second part I will make a connection of this Talbot effect with turbulence through the Schrodinger map which is a geometric non-linear partial differential equation.

Dynamics of inertial particles with memory: an application of fractional calculus

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Mohammad Farazmand – GA Tech Physics
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. I discuss the governing equations of motion for the inertial particles, i.e. the Maxey-Riley equation, including a fractional order derivative in time. Then I show that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is O(\epsilon)-close to the fluid velocity, where 0<\epsilon<<1 is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity.

Localization sequences in the algebraic K-theory of ring spectra

Series
Geometry Topology Seminar
Time
Monday, November 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Gepner – Purdue University
The algebraic K-theory of the sphere spectrum, K(S), encodes significant information in both homotopy theory and differential topology. In order to understand K(S), one can apply the techniques of chromatic homotopy theory in an attempt to approximate K(S) by certain localizations K(L_n S). The L_n S are in turn approximated by the Johnson-Wilson spectra E(n) = BP[v_n^{-1}], and it is not unreasonable to expect to be able to compute K(BP). This would lead inductively to information about K(E(n)) via the conjectural fiber sequence K(BP) --> K(BP) --> K(E(n)). In this talk, I will explain the basics of the K-theory of ring spectra, define the ring spectra of interest, and construct some actual localization sequences in their K-theory. I will then use trace methods to show that it the actual fiber of K(BP) --> K(E(n)) differs from K(BP), meaning that the situation is more complicated than was originally hoped. All this is joint work with Ben Antieau and Tobias Barthel.

Moduli of Tropical Plane Curves

Series
Algebra Seminar
Time
Friday, November 14, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Ralph Morrison – Berkeley
Smooth curves in the tropical plane correspond to unimodulartriangulations of lattice polygons. The skeleton of such a curve is ametric graph whose genus is the number of lattice points in the interior ofthe polygon. In this talk we report on work concerning the followingrealizability problem: Characterize all metric graphs that admit a planarrepresentation as a smooth tropical curve. For instance, about 29.5 percentof metric graphs of genus 3 have this property. (Joint work with SarahBrodsky, Michael Joswig, and Bernd Sturmfels.)

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