Seminars and Colloquia by Series

Geometric inequalities via information theory

Series
High Dimensional Seminar
Time
Wednesday, September 11, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jing Hao – Georgia Tech –

Using ideas from information theory, we establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions.  In the first part of the talk, we derive volume bounds for convex bodies using generalized subadditivity properties of entropy combined with entropy bounds for log-concave random variables. In the second part, we investigate a new notion of Fisher information which we call the L1-Fisher information and show that certain superadditivity properties of the L1-Fisher information lead to lower bounds for the surface areas of polyconvex sets in terms of its slices.

Unfoldings of 3D Polyhedra

Series
Geometry Topology Student Seminar
Time
Wednesday, September 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nicholas Barvinok –

Cutting a polyhedron along some spanning tree of its edges will yield an isometric immersion of the polyhedron into the plane. If this immersion is also injective, we call it an unfolding. In this talk I will give some general results about unfoldings of polyhedra. There is also a notion of pseudo-edge unfolding, which involves cutting on a pseudo edge graph, as opposed to an edge graph. A pseudo edge graph is a 3-connected graph on the surface of the polyhedron, whose vertices coincide with the vertices of the polyhedron, and whose edges are geodesics. I will explain part of the paper "Pseudo-Edge Unfoldings of Convex Polyhedra," a joint work of mine with Professor Ghomi, which proves the existence of a convex polyhedron with a pseudo edge graph along which it is not unfoldable. Finally, I will discuss some connections between pseudo edge graphs and edge graphs. 

\ell^p improving and sparse inequalities for averages along the square integers

Series
Analysis Seminar
Time
Wednesday, September 11, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rui Han – Georgia Tech

Let $f$ be defined on $\mathbb{Z}$. Let $A_N f$ be the average of $f$ along the square integers. 

We show that $A_N$ satisfies a local scale-free $\ell^{p}$-improving estimate, for $3/2

This parameter range is sharp up to the endpoint. We will also talk about sparse bounds for the maximal function 
$A f =\sup _{N\geq 1} |A_Nf|$. This work is based on a joint work with Michael T. Lacey and Fan Yang.

The geometry of phylogenetic tree spaces

Series
Mathematical Biology Seminar
Time
Wednesday, September 11, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bo Lin – Georgia Tech

Phylogenetic trees  are  the fundamental  mathematical  representation  of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the  complication that  their  discrete  geometric  structure  results  in  a  non-Euclidean phylogenetic  tree  space,  which  poses  computational  and   statistical limitations.

In this  talk, I  will compare  the geometric  and statistical  properties between a  well-studied framework  -  the BHV  space, and  an  alternative framework that  we  propose, which  is  based on  tropical  geometry.  Our framework exhibits analytic,  geometric, and  topological properties  that are desirable for  theoretical studies in  probability and statistics,  as well  as  increased  computational  efficiency.  I  also  demonstrate  our approach on an example of seasonal influenza data.

Mathematical Approaches to Image Processing and Data Understanding

Series
Undergraduate Seminar
Time
Monday, September 9, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Sung Ha Kang – Georgia Tech

Starting from Total Variation, this talk will overview some mathematical approaches for image processing, such as removing noise.  We will also consider numerical application to data understanding. A few more application maybe presented.

Link Concordance and Groups

Series
Geometry Topology Seminar
Time
Monday, September 9, 2019 - 14:00 for
Location
Speaker
Miriam Kuzbary – Georgia Tech –

This is a general audience Geometry-Topology talk where I will give a broad overview of my research interests and techniques I use in my work.  My research concerns the study of link concordance using groups, both extracting concordance data from group theoretic invariants and determining the properties of group structures on links modulo concordance. Milnor's invariants are one of the more fundamental link concordance invariants; they are thought of as higher order linking numbers and can be computed using both Massey products (due to Turaev and Porter) and higher order intersections (due to Cochran). In my work, I have generalized Milnor's invariants to knots inside a closed, oriented 3-manifold M. I call this the Dwyer number of a knot and show methods to compute it for null-homologous knots inside a family of 3-manifolds with free fundamental group. I further show Dwyer number provides the weight of the first non-vanishing Massey product in the knot complement in the ambient manifold. Additionally, I proved the Dwyer number detects knots K in M bounding smoothly embedded disks in specific 4-manifolds with boundary M which are not concordant to the unknot in M x I. This result further motivates my definition of a new link concordance group in joint work with Matthew Hedden using the knotification construction of Ozsv'ath and Szab'o. Finally, I will briefly discuss my recent result that the string link concordance group modulo its pure braid subgroup is non-abelian.

Newton polygons and zeroes of polynomials

Series
Student Algebraic Geometry Seminar
Time
Monday, September 9, 2019 - 13:15 for 1 hour (actually 50 minutes)
Location
Skiles 254
Speaker
Trevor Gunn – Georgia Tech

We will define Newton polygons for polynomials over a valued field and prove a couple theorems using them. For example, relating the valuations of the roots of the polynomial to the slopes of the Newton polygon and proving the algebraic closure of the Puiseux series in characteristic 0.

Differential Privacy: The Census Algorithm

Series
ACO Student Seminar
Time
Friday, September 6, 2019 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Samantha Petti – CS, Georgia Tech –

For the first time in 2020, the US Census Bureau will apply a differentially private algorithm before publicly releasing decennial census data. Recently, the Bureau publicly released their code and end-to-end tests on the 1940 census data at various privacylevels. We will outline the DP algorithm (which is still being developed) and discuss the accuracy of these end-to-end tests. In particular, we focus on the bias and variance of the reported population counts. Finally, we discuss the choices the Bureau has yet to make that will affect the balance between privacy and accuracy. This talk is based on joint work with Abraham Flaxman.

The Combinatorial Nullstellensatz and its applications

Series
Graph Theory Working Seminar
Time
Thursday, September 5, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Youngho Yoo – Georgia Tech

Please Note:

In 1999, Alon proved the “Combinatorial Nullstellensatz” which resembles Hilbert’s Nullstellensatz and gives combinatorial structure on the roots of a multivariate polynomial. This method has numerous applications, most notably in additive number theory, but also in many other areas of combinatorics. We will prove the Combinatorial Nullstellensatz and give some of its applications in graph theory.

 

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