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Series: Algebra Seminar

The conjectures of Green—Griffths—Lang predict the precise
interplay between different notions of hyperbolicity: Brody hyperbolic,
arithmetically hyperbolic, Kobayashi hyperbolic, algebraically
hyperbolic, groupless,
and more. In his thesis (1993), W.~Cherry defined a notion of
non-Archimedean hyperbolicity; however, his definition does not seem to
be the ``’correct’ version, as it does not mirror complex
hyperbolicity.
In recent work, A.~Javanpeykar and A.~Vezzani introduced a new
non-Archimedean notion of hyperbolicity, which ameliorates this issue,
and also stated a non-Archimedean variant of the Green—Griffths—Lang
conjecture.
In this talk, I will discuss
complex and non-Archimedean notions of hyperbolicity as well as some
recent progress on the non-Archimedean Green—Griffths—Lang conjecture.
This is joint work with Ariyan Javanpeykar (Mainz)
and Alberto Vezzani (Paris 13).

Series: Geometry Topology Seminar

I will discuss knot concordances in 3-manifolds. In particular I will talk about knot concordances of knots in the free homotopy class of S^1 x {pt} in S^1 x S^2. It turns out, we can use some of these concordances to construct Akbulut-Ruberman type exotic 4-manifolds. As a consequence, at the end of the talk we will see absolutely exotic Stein pair of 4-manifolds. This is joint work with Selman Akbulut.

Series: Geometry Topology Seminar

In this talk, we describe some applications of link Floer homology to the topology of surfaces in 4-space. If K is a knot in S^3, we will consider the set of surfaces in B^4 which bound K. This space is naturally endowed with a plethora of non-Euclidean metrics and pseudo-metrics. The simplest such metric is the stabilization distance, which is the minimum k such that there is a stabilization sequence connecting two surfaces such that no surface in the sequence has genus greater than k. We will talk about how link Floer homology can be used to give lower bounds, as well as some techniques for computing non-trivial examples. This is joint work with Andras Juhasz.

Series: Mathematical Biology Seminar

Vaccination is an effective method to protect against infectious diseases. An important
consideration in any vaccine formulation is the inoculum dose, i.e., amount of antigen or
live attenuated pathogen that is used. Higher levels generally lead to better stimulation
of the immune response but might cause more severe side effects and allow for less
population coverage in the presence of vaccine shortages. Determining the optimal
amount of inoculum dose is an important component of rational vaccine design. A
combination of mathematical models with experimental data can help determine the
impact of the inoculum dose. We designed mathematical models and fit them to data
from influenza A virus (IAV) infection of mice and human parainfluenza virus (HPIV) of
cotton rats at different inoculum doses. We used the model to predict the level of
immune protection and morbidity for different inoculum doses and to explore what an
optimal inoculum dose might be. We show how a framework that combines
mathematical models with experimental data can be used to study the impact of
inoculum dose on important outcomes such as immune protection and morbidity. We
find that the impact of inoculum dose on immune protection and morbidity depends on
the pathogen and both protection and morbidity do not always increase with increasing
inoculum dose. An intermediate inoculum dose can provide the best balance between
immune protection and morbidity, though this depends on the specific weighting of
protection and morbidity. Once vaccine design goals are specified with required levels
of protection and acceptable levels of morbidity, our proposed framework which
combines data and models can help in the rational design of vaccines and
determination of the optimal amount of inoculum.

Series: Analysis Seminar

We are going to discuss some recent results pertaining to the Falconer distance conjecture, including the joint paper with Guth, Ou and Wang establishing the $\frac{5}{4}$ threshold in the plane. We are also going to discuss the extent to which the sharpness of our method and similar results is tied to the distribution of lattice points on convex curves and surfaces.

Wednesday, January 30, 2019 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
Organizer: Surena Hozoori

In this series of (3-5) lectures, I will talk about different aspects of a class of contact 3-manifolds for which geometry, dynamics and topology interact subtly and beautifully. The talks are intended to include short surveys on "compatibility", "Anosovity" and "Conley-Zehnder indices". The goal is to use the theory of Contact Dynamics to show that conformally Anosov contact 3-manifolds (in particular, contact 3-manifolds with negative α-sectional curvature) are universally tight, irrducible and do not admit a Liouville cobordism to tight 3-sphere.

Series: High Dimensional Seminar

We shall survey a variety of results, some recent, some going back a long time, where combinatorial methods are used to prove or disprove the existence of orthogonal exponential bases and Gabor bases. The classical Erdos distance problem and the Erdos Integer Distance Principle play a key role in our discussion.

Series: Other Talks

This is a SCMB MathBioSys Seminar posted on behalf of Melissa Kemp (GT BME)

Constriction of blood vessels in the extremities due to traumatic injury to halt excessive blood loss or resulting from pathologic occlusion can cause considerable damage to the surrounding tissues with significant morbidity and mortality. Optimal healing of damaged tissue relies on the precise balance of pro-inflammatory and pro-healing processes of innate inflammation. In this talk, we will present a discrete multiscale mathematical model that spans the tissue and intracellular scales, and captures the consequences of targeting various regulatory components. We take advantage of the canalization properties of some of the functions, which is a type of hierarchical clustering of the inputs, and use it as control to steer the system away from a faulty attractor and understand better the regulatory relations that govern the system dynamics.EDIT: CANCELLED

Series: Job Candidate Talk

There has been high scientific interest to understand the behavior of the surface quasi-geostrophic (SQG) equation because it is a possible model to explain the formation of fronts of hot and cold air and because it also exhibits analogies with the 3D incompressible Euler equations. It is not known at this moment if this equation can produce singularities or if solutions exist globally. In this talk I will discuss some recent works on the existence of global solutions.

Series: Intersection Theory Seminar

We will finish chapter 7 of Eisenbud and Harris, 3264 and All That.Topics: Inflection points of curves in P^r, nets of plane curves, the topological Hurwitz formula.

Series: Stochastics Seminar

We discuss a problem of asymptotically efficient (that is, asymptotically normal with minimax optimal limit variance) estimation of functionals of the form $\langle f(\Sigma), B\rangle$ of unknown covariance $\Sigma$ based on i.i.d.mean zero Gaussian observations $X_1,\dots, X_n\in {\mathbb R}^d$ with covariance $\Sigma$. Under the assumptions that the dimension $d\leq n^{\alpha}$ for some $\alpha\in (0,1)$ and $f:{\mathbb R}\mapsto {\mathbb R}$ is of smoothness $s>\frac{1}{1-\alpha},$ we show how to construct an asymptotically
efficient estimator of such functionals (the smoothness threshold
$\frac{1}{1-\alpha}$ is known to be optimal for a simpler problem of
estimation of smooth functionals of unknown mean of normal
distribution).
The proof of this result relies on a variety of probabilistic and
analytic tools including Gaussian concentration, bounds on the
remainders of Taylor expansions of operator functions and bounds on
finite differences of smooth functions along certain Markov chains in
the spaces of positively semi-definite matrices.

Friday, February 1, 2019 - 12:00 ,
Location: Skiles 006 ,
Tianyi Zhang ,
Georgia Tech ,
Organizer: Trevor Gunn

Series: ACO Student Seminar

(The talk will be at 1-2pm, then it follows by a discussion session from 2 pm to 2:45 pm.)Powerful AI systems, which are driven by machine learning, are
increasingly controlling various aspects of modern society: from
social interactions (e.g., Facebook, Twitter, Google, YouTube),
economics (e.g., Uber, Airbnb, Banking), learning (e.g., Wikipedia,
MOOCs), governance (Judgements, Policing, Voting), to autonomous
vehicles and weapons. These systems have a tremendous potential to
change our lives for the better, but, via the ability to mimic and
nudge human behavior, they also have the potential to be
discriminatory, reinforce societal prejudices, and polarize opinions.
Moreover, recent studies have demonstrated that these systems can be
quite brittle and generally lack the required robustness to be
deployed in various civil/military situations. The reason being that
considerations such as fairness, robustness, stability,
explainability, accountability etc. have largely been an afterthought
in the development of AI systems. In this talk, I will discuss the
opportunities that lie ahead in a principled and thoughtful
development of AI systems.
Bio
Nisheeth Vishnoi is a Professor of Computer Science at Yale University.
He received a B.Tech in Computer Science and Engineering from IIT
Bombay in 1999 and a Ph.D. in Algorithms, Combinatorics and
Optimization from Georgia Tech in 2004. His research spans several
areas of theoretical computer science: from approximability of NP-hard
problems, to combinatorial, convex and non-convex optimization, to
tackling algorithmic questions involving dynamical systems, stochastic
processes and polynomials. He is also broadly interested in
understanding and addressing some of the key questions that arise in
nature and society from the viewpoint of theoretical computer science.
Here, his current focus is on natural algorithms, emergence of
intelligence, and questions at the interface of AI, ethics, and
society. He was the recipient of the Best Paper Award at FOCS in 2005,
the IBM Research Pat Goldberg Memorial Award in 2006, the Indian
National Science Academy Young Scientist Award in 2011, and the IIT
Bombay Young Alumni Achievers Award in 2016.

Series: Geometry Topology Seminar

The notion of an acylindrically hyperbolic group was introduced by Osin as a
generalization of non-elementary hyperbolic and relative hyperbolic groups. Ex-
amples of acylindrically hyperbolic groups can be found in mapping class groups,
outer automorphism groups of free groups, 3-manifold groups, etc. Interesting
properties of acylindrically hyperbolic groups can be proved by applying techniques such as Monod-Shalom rigidity theory, group theoretic Dehn filling, and
small cancellation theory. We have recently shown that non-elementary convergence groups are acylindrically hyperbolic. This result opens the door for
applications of the theory of acylindrically hyperbolic groups to non-elementary
convergence groups. In addition, we recovered a result of Yang which says a
finitely generated group whose Floyd boundary has at least 3 points is acylindrically hyperbolic.

Friday, February 1, 2019 - 15:05 ,
Location: Skiles 246 ,
Joan Gimeno ,
BGSMath-UB ,
Organizer: Jiaqi Yang

A real Taylor-Fourier expression is a Taylor expression whose coefficients are real Fourier series. In this talk we will discuss different numerical methods to compute the composition of two Taylor-Fourier expressions. To this end, we will show some possible implementations and we are going to discuss and show some results in performance. In particular, we are going to cover how the compositon of two Fourier series can be perfomed in logarithmic complexity.