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 Events
MIT
Mon 15 Jan 2018, 2:00pm SPECIAL
Topology and related seminars
ESB 4127
Floer transport and Lagrangian non-Abelianization
ESB 4127
Mon 15 Jan 2018, 2:00pm-3:00pm

Abstract

In this talk I will explain how to endow the moduli space of objects in certain wrapped Fukaya categories with a cluster structure. This will be achieved by counts of holomorphic disks between Lagrangians which are described by trivalent graphs. In particular, we will be recovering the Fock-Goncharov coordinates on the moduli space of flat connections on a surface and provide a symplectic interpretation for the non-Abelianization procedure via spectral networks.
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Cornell Physics and Mechanical & Aerospace Engineering
Mon 15 Jan 2018, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
From Newton's Law to Neurons
ESB 2012
Mon 15 Jan 2018, 3:00pm-4:00pm

Abstract

 Intended Audience: Public

 
Insects are first evolved to fly, and to fly is not to fall. How does an insect fly, why does it fly so well, and how can we infer its ‘thoughts’ from its flight dynamics? We have been seeking mechanistic explanations of the complex movement of insect flight. Starting from the Navier-Stokes equations governing the unsteady aerodynamics of flapping flight, we worked to build a theoretical framework for computing flight. This has led to new interpretations and predictions of the functions of an insect’s internal machinery that orchestrate its flight. I will discuss our recent computational and experimental studies of the balancing act of dragonflies and fruit flies: how a dragonfly recovers from falling upside-down and how a fly balances in air. In each case, the physics of flight informs us about the neural feedback circuitries underlying their fast reflexes.

Note for Attendees

There will be a reception before the talk in ESB 4133 (the PIMS lounge). This is a talk in the IAM/PIMS distinguished series.  
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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, 4:00pm-5:00pm

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.

Note for Attendees

Refreshments will be served before this colloquium in MATH 125, the Math Lounge area, at 3:45 p.m.
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Oregon
Mon 15 Jan 2018, 5:00pm SPECIAL
Algebraic Geometry Seminar
Math 126 (note special time)
CANCELED - Exoflops
Math 126 (note special time)
Mon 15 Jan 2018, 5:00pm-6:00pm

Abstract

Consider a contraction pi: X -> Y from a smooth Calabi-Yau 3-fold to a singular one. (This is half of an "extremal transition;" the other half would be a smoothing of Y.) In many examples there is an intermediate object called an "exoflop" -- a category of matrix factorizations, derived-equivalent to X, where the critical locus of the superpotential looks like Y with a P^1 sticking out of it, and objects of D(X) that will be killed by pi_* correspond to objects supported at the far end of the P^1. I will discuss one or two interesting examples. This is joint work with Paul Aspinwall.
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Timm Treskatis
Mathematics, UBC
Tue 16 Jan 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
From Convex Optimisation to High-Resolution Finite Elements: Simulating Reactive Viscoplastic Fluid Flows
ESB 4133 (PIMS Lounge)
Tue 16 Jan 2018, 12:30pm-1:30pm

Abstract

What if we could imitate spider silk glands to produce biodegradable materials with properties similar to rubber or plastic? In our interdisciplinary team of fluid dynamicists, chemical engineers and material scientists, my role as mathematician is to try and answer this question from the numerical perspective. In this context, I am working on a problem of multiphase flow that includes advection, diffusion, chemical reaction, osmosis and viscoplastic behavior.

When it comes to the numerical solution of such a model that is based on a real-life problem, I am a strong advocate of so-called mimetic methods, i.e. discretisation schemes which preserve the physical properties of the system also at the discrete level. Following this philosophy,
* the transition between viscous flow and plastic creep is treated in a genuinely nonsmooth fashion and not simply smoothed out,
* the discretisation of the Navier-Stokes equations is pressure-robust,
* conservation of mass and momentum are respected,
* maximum principles are preserved,
* numerical diffusion is limited to an absolute minimum.

Additionally, the algorithm should clearly be stable, efficient and accurate for both steady and unsteady flow problems.

In this talk, I will show how we can couple fast algorithms from convex optimisation, a finite-element discretisation and algebraic flux correction to attain these objectives. Some videos of various flow configurations are included as well! 
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Nicolau Sarquis Aiex
UBC & PIMS
Tue 16 Jan 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
The space of min-max hypersurfaces
ESB 2012
Tue 16 Jan 2018, 3:30pm-4:30pm

Abstract

We use Lusternik-Schnirelmann Theory to study the topology of the space of closed embedded minimal hypersurfaces on a manifold of dimension between 3 and 7 and positive Ricci curvature. Combined with the works of Marques-Neves we can also obtain some information on the geometry of the minimal hypersurfaces they found.
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University of Auckland
Wed 17 Jan 2018, 3:10pm
Probability Seminar
LSK 460
The gaps left by a Brownian motion
LSK 460
Wed 17 Jan 2018, 3:10pm-4:10pm

Abstract


Run a Brownian motion on a torus for a long time.  How large are the

random gaps left behind when the path is removed?

 

In three (or more) dimensions, we find that there is a deterministic spatial

scale common to all the large gaps anywhere in the torus.  Moreover, we can

identify whether a gap of a given shape is likely to exist on this scale, in

terms of a single parameter, the classical (Newtonian) capacity.  I will

describe why this allows us to identify a well-defined "component" structure in

our random porous set.


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Oxford University
Thu 18 Jan 2018, 11:00am SPECIAL
Mathematical Biology Seminar / Probability Seminar
Math 126
Modelling mutations: mechanisms and evolutionary consequences
Math 126
Thu 18 Jan 2018, 11:00am-12:00pm

Abstract

 As the source of new genetic variation, mutations constitute a fundamental process in evolution. While most mutations lower fitness, rare beneficial mutations are essential for adaptation to changing environments. Thus, understanding the effects of mutations and estimating their rate is of strong interest in evolutionary biology. The necessity to treat rare mutational events stochastically has also stimulated a rich mathematical literature. Typically, mutations are modelled simply as an instantaneous change of type, occurring at a fixed rate. However, the underlying biology is more complex. I will present two recent projects delving deeper into mutational mechanisms and their consequences. Firstly, mutations can exhibit a multi-generational delay in phenotypic expression. Secondly, individuals within a population can vary in their propensity to mutate. Through analytical and simulation methods, we investigated the impact of these biological complexities on (a) population fitness and capacity to evolve, and (b) our ability to accurately infer mutation rates from data. I will conclude by discussing some future directions to incorporate these insights into more realistic models and to quantify the distribution of mutation rate empirically.

Note for Attendees

 Math 126 is behind a locked glass door. Latecomers without access should knock loudly!
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Kornelia Hera
Eotvos Lorand University, Budapest
Fri 19 Jan 2018, 2:00pm
Harmonic Analysis Seminar
MATH 126
Furstenberg-type estimates for unions of affine subspaces
MATH 126
Fri 19 Jan 2018, 2:00pm-3:00pm

Abstract

A plane set is called a t-Furstenberg set for some t in (0,1), if it has an at least t-dimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension).  Classical results are that every t-Furstenberg set has dimension at least 2t, and at least t + 1/2.

We generalize these estimates for families of affine subspaces. As a result, we prove that the union of any s-dimensional family of k-dimensional affine subspaces is at least k + s/(k+1) -dimensional, and is exactly k + s -dimensional if s is at most 1.

Based on joint work with Tamas Keleti and Andras Mathe.
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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, 3:00pm-4:00pm

Abstract

Biological populations facing severe environmental change must adapt in order to avoid extinction. This so-called “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 well-adapted 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 (non-extinction) of new lineages, using antibiotic-resistant 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.

Note for Attendees

Refreshments will be served at 2:45 p.m. in ESB 4133, the PIMS Lounge.
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