Columbia University

Fri 20 Jan 2017, 3:00pm
Department Colloquium
seminar has been cancelled.

CANCELLED: Singular Stochastic Partial Differential Equations  How do they arise and what do they mean?

seminar has been cancelled.
Fri 20 Jan 2017, 3:00pm4:00pm
Abstract
Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
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Toronto

Mon 23 Jan 2017, 3:00pm
SPECIAL
Institute of Applied Mathematics
ESB 2012

TBA

ESB 2012
Mon 23 Jan 2017, 3:00pm4:00pm
Abstract
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Max Planck Institute Bonn

Tue 24 Jan 2017, 3:00pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
MATH 126

Chiral differential operators and the curved betagamma system

MATH 126
Tue 24 Jan 2017, 3:00pm4:00pm
Abstract
Chiral differential operators (CDOs) are a vertex algebra analog of the associative algebra of differential operators. Originally introduced by mathematicians, Witten explained how CDOs arise as the perturbative part of the curved betagamma system with target X. I will describe recent work with Gorbounov and Williams in which we construct the BV quantization of this theory and use a combination of factorization algebras and formal geometry to recover CDOs. At the end, I hope to discuss how the techniques we developed apply to a broad class of nonlinear sigma models, including source manifolds of higher dimension.
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UBC

Wed 25 Jan 2017, 1:45pm
Mathematical Biology Seminar
PIMS

Multiscale modeling of vesicular release at neuronal synapses.

PIMS
Wed 25 Jan 2017, 1:45pm2:45pm
Abstract
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. I will present in this talk a hybrid discretecontinuum model that takes into account both a stochastic regime governed by rare events and a continuous regime in the bulk, in the context of vesicular release at chemical synapses.
In a first part, I computed the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. This models the binding of calcium ions on the SNARE complex, a process that triggers vesicular release. Using this result, I developed a model to study how vesicles and calcium channels organization shape such process.
In a second part, I will present a model for the presynaptic terminal built using the results described above. This model was formulated in an initial stage as a reactiondiffusion problem in a confined microdomain, where Brownian particles have to bind to small target sites. I coarsegrained this model into a system of mass action equations coupled to a set of Markov equations, which allows to obtain analytical results and to realize fast stochastic simulations.
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Max Planck Institute Bonn

Wed 25 Jan 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012 (note special day)

From Feynman diagrams to commutative diagrams

ESB 2012 (note special day)
Wed 25 Jan 2017, 3:00pm4:00pm
Abstract
Factorization algebras are localtoglobal objects that play a role in quantum field theory akin to the role of sheaves in geometry: they conveniently organize complicated information. In the talk I will introduce this notion, give some concrete examples, and then explain how factorization algebras mediate between QFT and higher algebra. An important example will be ChernSimons theory; ongoing work with Costello and Francis recovers quantum groups with formal parameter by combining Koszul duality with Feynman diagrams.
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University of Chicago

Wed 25 Jan 2017, 4:15pm
SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)

Quantitative Nullcobordism and the (in)effectiveness of algebraic topology.

ESB 4133 (PIMS Lounge)
Wed 25 Jan 2017, 4:15pm5:15pm
Abstract
Topology is full of ineffective arguments constructing objects and equivalences by algebra.
One of the great early achievements of algebraic topology was the work of Thom, followed by Milnor and Wall, on cobordism theory, which describes when a compact smooth (oriented) manifold is the boundary of some compact manifold with boundary. This method is typical of the problems that arise in the use of algebraic methods and is an early example of one of the dominant philosophies of geometric topology. The question we study is to what extent the complexity of a manifold can be used to bound, when it exists, the minimum necessary complexity of something that it bounds.
The goal of this talk is to explain generally some of the issues of making topology less ineffective.
We shall show that there are polynomial size nullcobordisms in a suitable sense. This is joint work with Greg Chambers, Dominic Dotterer and Fedor Manin.
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Note for Attendees
Reception preceding the talk in ESB 4133 (the PIMS lounge). This is part of the IAM/PIMS distinguished colloquium series.