MIT

Mon 15 Jan 2018, 4:00pm
SPECIAL
Department Colloquium
MATH 100 (note special time and place)

The symplectic topology of affine varieties

MATH 100 (note special time and place)
Mon 15 Jan 2018, 4:00pm5:00pm
Abstract
In this talk we will study complex affine varieties via symplectic topology. First, I will explain how to describe their complex structures, up to deformation, using Legendrian knots. Second, we will focus on the study of these Legendrian knots and provide techniques to distinguish them or show they are isotopic. Then, we will apply them to obtain new results about complex affine manifolds. In particular, we will recover the mirror symmetry functor from the perspective of Legendrian knot theory.
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Oxford University

Fri 19 Jan 2018, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

Stochastic population dynamic models with applications to pathogen evolution

ESB 2012
Fri 19 Jan 2018, 3:00pm4:00pm
Abstract
Biological populations facing severe environmental change must adapt in order to avoid extinction. This socalled “evolutionary rescue” scenario is relevant to many applied problems, including pathogen evolution of drug resistance during the treatment of infectious diseases. Understanding what drives the rescue process gives rise to interesting mathematical modelling challenges arising from two key features: demographic and evolutionary processes occur on the same timescale, and stochasticity is inherent in the emergence of rare welladapted mutants. In this talk, I will present recent work on population dynamics in changing environments, merging biological realism with tractable stochastic models. Firstly, I will describe a model of drug resistance evolution in chronic viral infections, which serves as a case study for a novel mathematical approach yielding analytical approximations for the probability of rescue. Secondly, I will present a combined theoretical and experimental investigation of the classical problem of establishment (nonextinction) of new lineages, using antibioticresistant bacteria as a model system. Finally, I will discuss some future directions in modelling antibiotic treatment to predict optimal dosing strategies, and in developing a general theoretical framework for evolutionary rescue that unites approaches to distinct applied problems.
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Seminar Information Pages

Note for Attendees
Refreshments will be served before this colloquium in MATH 125, the Math Lounge area, at 3:45 p.m.