Seminars and Colloquia by Series

Wednesday, September 19, 2018 - 16:30 , Location: Skiles 006 , Dantong Zhu , Georgia Tech , Organizer: Xingxing Yu
An $r$-cut of a $k$-uniform hypergraph $H$ is a partition of the vertex set of $H$ into $r$ parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every $m$-edge graph has a 2-cut of size $m/2+\Omega(\sqrt{m})$, and this is best possible. In this talk we will discuss recent results on analogues of Edwards’ result and related problems in hypergraphs.
Wednesday, September 19, 2018 - 16:00 , Location: Skiles 005 , Michael Loss , School of Mathematics, Georgia Tech , loss@math.gatech.edu , Organizer: Michael Loss
We introduce a quantum version of the Kac Master equation,and we explain issues like equilibria, propagation of chaos and the corresponding quantum Boltzmann equation. This is joint work with Eric Carlen and Maria Carvalho.
Wednesday, September 19, 2018 - 14:00 , Location: Skiles 006 , Hyunki Min , Georgia Tech , Organizer: Hyun Ki Min
In 1957, Smale proved a striking result: we can turn a sphere inside out without any singularity. Gromov in his thesis, proved a generalized version of this theorem, which had been the starting point of the h-principle. In this talk, we will prove Gromov's theorem and see applications of it.
Wednesday, September 19, 2018 - 13:55 , Location: Skiles 005 , Marcin Bownik , University of Oregon , Organizer: Shahaf Nitzan
In this talk we shall explore some of the consequences of the solution to the Kadison-Singer problem. In the first part of the talk we present results from a joint work with Itay Londner. We show that every subset $S$ of the torus of positive Lebesgue measure admits a Riesz sequence of exponentials $\{ e^{i\lambda x}\} _{\lambda \in \Lambda}$ in $L^2(S)$ such that $\Lambda\subset\mathbb{Z}$ is a set with gaps between consecutive elements bounded by $C/|S|$. In the second part of the talk we shall explore a higher rank extension of the main result of Marcus, Spielman, and Srivastava, which was used in the solution of the Kadison-Singer problem.
Wednesday, September 19, 2018 - 12:55 , Location: Skiles 006 , Han Huang , University of Michigan , sthhan@umich.edu , Organizer: Konstantin Tikhomirov
It is natural to question whether the center of mass of a convex body $K\subset \mathbb{R}^n$ lies in its John ellipsoid $B_K$, i.e., in the maximal volume ellipsoid contained in $K$. This question is relevant to the efficiency of many algorithms for convex bodies. We obtain an unexpected negative result. There exists a convex body $K\subset \mathbb{R}^n$ such that its center of mass does not lie in the  John ellipsoid $B_K$  inflated $(1-o(1))n$ times about the center of $B_K$. (Yet, if one inflate $B_K$ by a factor $n$, it contains $K$.)Moreover, there exists a polytope $P \subset \mathbb{R}^n$ with $O(n^2)$ facets whose center of mass is not contained in the John ellipsoid  $B_P$ inflated $O(\frac{n}{\log(n)})$ times about the center of $B_P$.
Wednesday, September 19, 2018 - 12:20 , Location: Skiles 005 , Blair Sullivan , North Carolina State University , blair_sullivan@ncsu.edu , Organizer: Trevor Gunn
In this talk, we describe transforming a theoretical algorithm from structural graph theory into open-source software being actively used for real-world data analysis in computational biology. Specifically, we apply the r-dominating set algorithm for graph classes of bounded expansion in the setting of metagenome analysis. We discuss algorithmic improvements required for a practical implementation, alongside exciting preliminary biological results (on real data!). Finally, we include a brief retrospective on the collaboration process. No prior knowledge in metagenomics or structural graph theory is assumed. Based on joint work with T. Brown, D. Moritz, M. O’Brien, F. Reidl and T. Reiter.
Monday, September 17, 2018 - 14:00 , Location: Skiles 006 , John Etnyre , Georgia Tech , Organizer: John Etnyre
The study of transverse knots in dimension 3 has been instrumental in the development of 3 dimensional contact ge- ometry. One natural generalization of transverse knots to higher dimensions is contact submanifolds. Embeddings of one contact manifold into another satisfies an h-principle for codimension greater than 2, so we will discuss the case of codimension 2 contact embeddings. We will give the first pair of non-isotopic contact embeddings in all dimensions (that are formally isotopic).
Monday, September 17, 2018 - 13:55 , Location: Skiles 005 , Professor Lourenco Beirao da Veiga , Università di Milano-Bicocca , Organizer: Haomin Zhou

This is a joint seminar by College of Engineering and School of Math.

The Virtual Element Method (VEM), is a very recent technology introduced in [Beirao da Veiga, Brezzi, Cangiani, Manzini, Marini, Russo, 2013, M3AS] for the discretization of partial differential equations, that has shared a good success in recent years. The VEM can be interpreted as a generalization of the Finite Element Method that allows to use general polygonal and polyhedral meshes, still keeping the same coding complexity and allowing for arbitrary degree of accuracy. The Virtual Element Method makes use of local functions that are not necessarily polynomials and are defined in an implicit way. Nevertheless, by a wise choice of the degrees of freedom and introducing a novel construction of the associated stiffness matrixes, the VEM avoids the explicit integration of such shape functions.   In addition to the possibility to handle general polytopal meshes, the flexibility of the above construction yields other interesting properties with respect to more standard Galerkin methods. For instance, the VEM easily allows to build discrete spaces of arbitrary C^k regularity, or to satisfy exactly the divergence-free constraint for incompressible fluids.   The present talk is an introduction to the VEM, aiming at showing the main ideas of the method. We consider for simplicity a simple elliptic model problem (that is pure diffusion with variable coefficients) but set ourselves in the more involved 3D setting. In the first part we introduce the adopted Virtual Element space and the associated degrees of freedom, first by addressing the faces of the polyhedrons (i.e. polygons) and then building the space in the full volumes. We then describe the construction of the discrete bilinear form and the ensuing discretization of the problem. Furthermore, we show a set of theoretical and numerical results. In the very final part, we will give a glance at more involved problems, such as magnetostatics (mixed problem with more complex spaces interacting) and large deformation elasticity (nonlinear problem).  
Friday, September 14, 2018 - 15:00 , Location: Skiles 005 , Ernie Croot , Georgia Tech , Organizer: Lutz Warnke
An old question in additive number theory is determining the length of the longest progression in a sumset A+B = {a + b : a in A, b in B}, given that A and B are "large" subsets of {1,2,...,n}. I will survey some of the results on this problem, including a discussion of the methods, and also will discuss some open questions and conjectures.
Friday, September 14, 2018 - 14:00 , Location: Skiles 005 , Ethan Cotterill , Universidade Federal Fluminense , Organizer: Yoav Len
According to Plucker's formula, the total inflection of a linear series (L,V) on a complex algebraic curve C is fixed by numerical data, namely the degree of L and the dimension of V. Equipping C and (L,V) with compatible real structures, it is more interesting to ask about the total real inflection of (L,V). The topology of the real inflectionary locus depends in a nontrivial way on the topology of the real locus of C. We study this dependency when C is hyperelliptic and (L,V) is a complete series. We first use a nonarchimedean degeneration to relate the (real) inflection of complete series to the (real) inflection of incomplete series on elliptic curves; we then analyze the real loci of Wronskians along an elliptic curve, and formulate some conjectural quantitative estimates.

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