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Series: Dissertation Defense

We will present three results in percolation and sequence analysis. In the first part, we will briefly show an exponential concentration inequality for transversal fluctuation of directed last passage site percolation. In the the second part, we will dive into the power lower bounds for all the r-th central moments ($r\ge1$) of the last passage time of directed site perolcation on a thin box. In the last part, we will partially answer a conjecture raised by Bukh and Zhou that the minimal expected length of the longest common subsequences between two i.i.d. random permutations with arbitrary distribution on the symmetric group is obtained when the distribution is uniform and thus lower bounded by $c\sqrt{n}$ by showing that some distribution can be iteratively constructed such that it gives strictly smaller expectation than uniform distribution and a quick cubic root of $n$ lower bound will also be shown.

Series: AMS Club Seminar

Inkscape is an powerful open-source drawing program suitable for making
figures for your math papers and lectures. In this talk I will discuss
some of the useful tricks and features that you can take advantage of in
this
software, as well as some things to avoid. This will be a live demonstration talk, please bring a laptop if you can.

Series: Dissertation Defense

The curve complex of Harvey allows combinatorial representation of a surface mappingclass group by describing its action on simple closed curves. Similar complexes of spheres,free factors, and free splittings allow combinatorial representation of the automorphisms ofa free group. We consider a Birman exact sequence for combinatorial models of mappingclass groups and free group automorphisms. We apply this and other extension techniquesto compute the automorphism groups of several simplicial complexes associated with map-ping class groups and automorphisms of free groups.

Series: Stochastics Seminar

Random balls models are collections of Euclidean balls whose centers and radii are generated by a Poisson point process. Such collections model various contexts ranging from imaging to communication network. When the distributions driving the centers and the radii are heavy-tailed, interesting interference phenomena occurs when the model is properly zoomed-out. The talk aims to illustrate such phenomena and to give an overview of the asymptotic behavior of functionals of interest. The limits obtained include in particular stable fields, (fractional) Gaussian fields and Poissonian bridges. Related questions will also be discussed.

Series: Combinatorics Seminar

Series: School of Mathematics Colloquium

Given two complex polynomials, we can try to mathematically paste them
together to obtain a rational function through a procedure known as
mating the polynomials. In this talk, we will begin by trying to
understand the "shape" of complex polynomials in general. We will then
discuss the mating of two quadratic polynomials: we explore examples
where the mating does exist, and examples where it does not. There will
be lots of movies and exploration in this talk.

Wednesday, May 30, 2018 - 14:00 ,
Location: Skiles 006 ,
Tongzhou Chen ,
GT Math ,
Organizer: Jiaqi Yang

We model and analyze the dynamics of religious group membership
and size. A groups is distinguished by its strictness, which determines
how much time group members are expected to spend contributing to the
group. Individuals differ in their rate of return for time spent outside
of their religious group. We construct a utility function that individ-
uals attempt to maximize, then find a Nash Equilibrium for religious
group participation with a heterogeneous population. We then model
dynamics of group size by including birth, death, and switching of
individuals between groups. Group switching depends on the strictness
preferences of individuals and their probability of encountering members
of other groups.

Series: Geometry Topology Seminar

This will be a 90 minute seminar

It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties are preserved under various types of contact surgeries. The case for the negative contact surgeries is fairly well understood. In this talk, we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically/Stein fillable when r is in (0,1]. This is joint work with James Conway and John Etnyre.

Series: PDE Seminar

The ground state solution to the nonlinear Schrödinger equation (NLS) is a global, non-scattering solution that often provides a threshold between scattering and blowup. In this talk, we will discuss new, simplified proofs of scattering below the ground state threshold (joint with B. Dodson) in both the radial and non-radial settings.

Wednesday, May 2, 2018 - 14:00 ,
Location: Skiles 006 ,
Hyunki Min ,
Georgia Tech ,
hmin38@gatech.edu ,
Organizer:

Understanding contact structures on
hyperbolic 3-manifolds is one of the major open problems in the area of contact
topology. As a first step, we try to classify tight contact structures on a specific hyperbolic 3-manifold. In this talk, we will review the previous classification
results and classify tight contact structures on the Weeks manifold, which
has the smallest hyperbolic volume. Finally,
we will discuss how to generalize this method to classify tight contact structures
on some other hyperbolic 3-manifolds.