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Series: Algebra Seminar

TBA

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 - 12:00 ,
Location: Skiles 005 ,
Tianyi Zhang ,
Georgia Tech ,
Organizer: Trevor Gunn

Series: Stochastics Seminar

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: Job Candidate Talk

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: 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.

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: Geometry Topology Seminar