### Models for DNA-based Tile Self-Assembly

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 23, 2019 - 12:20 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Daniel Cruz – Georgia Tech

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- Series
- Research Horizons Seminar
- Time
- Wednesday, October 23, 2019 - 12:20 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Daniel Cruz – Georgia Tech

A set of elementary building blocks undergoes self-assembly if local interactions govern how this set forms intricate structures. Self-assembly has been widely observed in nature, ranging from the field of crystallography to the study of viruses and multicellular organisms. In this talk, we give an overview of tile assembly models (TAMs) whose elementary building blocks (i.e. tiles) are polygons which have been defined with rules for local interaction. In particular, we present the basic concepts associated with two of the most well-studied TAMs: the abstract Tile Assembly Model (aTAM) and the Two-Handed Assembly Model (2HAM). We show how TAMs are related to the problem of designing nanoscale structures with DNA. We also present some of the major results within this field of study.

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 9, 2019 - 13:10 for
- Location
- Skiles 005
- Speaker
- Larissa Serdukova – Georgia Tech – larissa.serdukova@math.gatech.edu

**Please Note:** NOTE THE UNUSUAL TIME: This seminar takes place from 1:10-1:50 for THIS WEEK ONLY.

Basin of attraction for a stable equilibrium point is an effective concept for stability in deterministic systems. However, it does not contain information on the external perturbations that may affect it. The concept of stochastic basin of attraction (SBA) is introduced by incorporating a suitable probabilistic notion of basin. The criteria for the size of the SBA is based on the escape probability, which is one of the deterministic quantities that carry dynamical information and can be used to quantify dynamical behavior of the corresponding stochastic basin of attraction. SBA is an efficient tool to describe the metastable phenomena complementing the known exit time, escape probability, or relaxation time. Moreover, the geometric structure of SBA gives additional insight into the system's dynamical behavior, which is important for theoretical and practical reasons. This concept can be used not only in models with small intensity but also with whose amplitude is proportional or in general is a function of an order parameter. The efficiency of the concept is presented through two applications.

- Series
- Research Horizons Seminar
- Time
- Wednesday, October 2, 2019 - 12:20 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Mohammad Ghomi – Georgia Tech – ghomi@math.gatech.edu

The classical isoperimetric inequality states that in Euclidean space spheres form the least perimeter enclosures for any give volume. We will review the historic development of this result in mathematics, and various approaches to proving it. Then we will discuss how one of these approaches, which is a variational argument, may be extended to spaces of nonpositive curvature, known as Cartan-Hadamard manifolds, in order to generalize the isoperimetric inequality.

- Series
- Research Horizons Seminar
- Time
- Wednesday, September 4, 2019 - 12:20 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Wade Bloomquist – Georgia Tech

We will explore some of the basic notions in quantum topology. Our focus will be on introducing some of the foundations of diagrammatic algebra through the lens of the Temperley-Lieb algebra. We will attempt to show how these diagrammatic techniques can be applied to low dimensional topology. Every effort will be made to make this as self-contained as possible. If time permits we will also discuss some applications to topological quantum computing.

- Series
- Research Horizons Seminar
- Time
- Wednesday, April 24, 2019 - 00:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Lutz Warnke – Georgia Tech

During the last 30 years there has been much interest in random graph processes, i.e., random graphs which grow by adding edges (or vertices) step-by-step in some random way. Part of the motivation stems from more realistic modeling, since many real world networks such as Facebook evolve over time. Further motivation stems from extremal combinatorics, where these processes lead to some of the best known bounds in Ramsey and Turan Theory (that go beyond textbook applications of the probabilistic method). I will review several random graph processes of interest, and (if time permits) illustrate one of the main proof techniques using a simple toy example.

- Series
- Research Horizons Seminar
- Time
- Wednesday, April 17, 2019 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Christian Houdré – Georgia Tech

I will briefly present our Stochastics Group and its main interests, and will continue with some of the problems I have worked on in recent years.

- Series
- Research Horizons Seminar
- Time
- Wednesday, April 3, 2019 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Leonid Bunimovich – Georgia Tech

Mathematical billiards naturally arise in mechanics, optics, acoustics, etc. They also form the most visual class of dynamical systems with evolution covering all the possible spectrum of behaviours from integrable (extremely regular) to strongly chaotic. Billiard is a (deterministic) dynamical system generated by an uniform (by inertia) motion of a point particle within a domain with piecewise smooth walls ("a billiard table"). I will introduce all needed notions on simple examples and outline some open problems. This talk is also a preparatory talk to a Mathematical Physics seminar (on Monday April 8) where a new direction of research will be discussed which consider physical billiards where instead of a point (mathematical) particle a real physical hard sphere moves. To a complete surprise of mathematicians and PHYSICISTS evolution of a billiard may completely change (and in different ways) in transition from mathematical to physical billiards. It a rare example when mathematicians surprise physicists. Some striking results with physicists are also already obtained. I will (again visually) explain at the end of RH why it is surprising that there could be difference between Math and Phys billiards.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 27, 2019 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Dan Margalit – Georgia Tech

An element of the braid group can be visualized as a collection of n strings that are braided (like a hair braid). Braid groups are ubiquitous in mathematics in science, as they record the motions of a number of points in the plane. These points can be autonomous vehicles, particles in a 2-dimensional medium, or roots of a polynomial. We will give an introduction to and a survey of braid groups, and discuss what is known about homomorphisms between braid groups.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 20, 2019 - 00:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jennifer Kloke – Ayasdi

The Mapper algorithm constructs compressed representations of the underlying structure of data but involves a large number of parameters. To make the Mapper algorithm accessible to domain experts, automation of the parameter selection becomes critical. This talk will be accessible to graduate students.

- Series
- Research Horizons Seminar
- Time
- Wednesday, February 13, 2019 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Josephine Yu – Georgia Tech

For a polytope P, the h-vector is a vector of integers which can be calculated easily from the number of faces of P of each dimension. For simplicial polytopes, it is well known that the h-vector is symmetric (palindromic) and unimodal. However in general the h-numbers may even be negative. In this talk I will introduce the tropical h-vector of a polytope, which coincides with the usual h-vector of the dual polytope, if the polytope is simple. We will discuss how they are related to toric varieties, tropical geometry, and polytope algebra. I will also discuss some open problems.

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