Mathematics Dept.
  Events
Ph.D. Candidate: Man Shun Ma
Mathematics, UBC
Mon 1 May 2017, 12:30pm SPECIAL
Room 202, Anthropology and Sociology Bldg (ANSOC) 6303 NW Marine Drive, UBC
Geometric properties of the space of Lagrangian self-shrinking tori in R^4
Room 202, Anthropology and Sociology Bldg (ANSOC) 6303 NW Marine Drive, UBC
Mon 1 May 2017, 12:30pm-2:30pm

Details

We prove that any sequence of conformally branched compact Lagrangian self-shrinkers in four dimensional Euclidean space with uniform area upper bound and fixed genus has a convergent subsequence, if the conformal structures do not degenerate. When the genus is one, we can drop the assumption on non-degeneracy the conformal structures. We also show that there is no branched immersion of Lagrangian self-shrinking sphere. When the area bound is small, we show that any such Lagrangian self-shrinking torus is embedded with uniform curvature estimates. For a general area bound, we prove that the entropy for the Lagrangian self-shrinking tori can only take finitely many values; this is done by deriving a Lojasiewicz-Simon type gradient inequality for the branched conformal self-shrinking tori.

Using the finiteness of entropy values, we construct a piecewise Lagrangian mean curvature flow for Lagrangian immersed tori, along which the Lagrangian condition is preserved, area is decreasing, and the compact type I singularities with a fixed area upper bound can be perturbed away in finitely many steps. This is a Lagrangian version of the construction for embedded surfaces by Colding-Minicozzi.

In the noncompact situation, we derive a parabolic Omori-Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on l-sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in Euclidean spaces with uniform bounded second fundamental form. This generalizes a result of Wang for compact immersions. We also prove an Omori-Yau maximum principle for properly immersed self-shrinkers.

Note for Attendees

Latecomers will not be admitted.
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Statistics SFU
Mon 1 May 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Possession Sketches: Mapping NBA Strategies
ESB 2012
Mon 1 May 2017, 3:00pm-4:00pm

Abstract

We present Possession Sketches, a new machine learning method for organizing and exploring a database of basketball player-tracks. Our method organizes basketball possessions by offensive structure. We first develop a model for populating a dictionary of short, repeated, and spatially registered actions. Each action corresponds to an interpretable type of player movement. We examine statistical patterns in these actions, and show how they can be used to describe individual player behavior. Leveraging this vocabulary of actions, we develop a hierarchical model that describes interactions between players. Our approach draws on the topic-modeling literature, extending Latent Dirichlet Allocation (LDA) through a novel representation of player movement data which uses techniques common in animation and video game design. We show that our model is able to group together possessions with similar offensive structure, allowing for efficient search and exploration of the entire database of player-tracking data. We show that our model finds repeated offensive structure in teams (e.g. strategy), providing a much more sophisticated, yet interpretable lens into basketball player-tracking data.

Note for Attendees

 This is a talk in the BC Data Colloquium. Reception beforehand in ESB 4133 (the PIMS lounge).
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Cédric Villani, Fields Medal Winner and TEDx alumni
Director of the Institut Henri Poincaré
Tue 2 May 2017, 7:00pm
Vogue Theatre, Vancouver
PIMS & Peter Wall Institute for Advanced Studies Public Lecture: The Hidden Beauty of Mathematics
Vogue Theatre, Vancouver
Tue 2 May 2017, 7:00pm-8:00pm

Details

It has been said that mathematics is the poetry of science. Some of the fundamental values of poetry parallel those of mathematics, and mathematical research is, in many ways, an art. Professor Cédric Villani will discuss the interface between mathematics and art, showing how both these disciplines seek to illuminate hidden beauty in the world.

Note for Attendees

This lecture with Cédric Villani is sold out. There will be a standby line available on the night of the lecture.
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Cédric Villani
Institut Henri Poincaré
Wed 3 May 2017, 3:00pm
ESB 1013, UBC
PIMS Math Seminar: Stability in some models of classical mathematical physics
ESB 1013, UBC
Wed 3 May 2017, 3:00pm-4:00pm

Details

Stability of classical mechanical systems is very old problem, still very much under scrutiny nowadays. Some techniques can be applied transversally in different problems.

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Cédric Villani is the Director of the Institut Henri Poincaré, France’s prime and oldest international institute for research in mathematical sciences. He has received many mathematical awards, including the Fields Medal in 2010, often considered the most prestigious in mathematics. Prof. Villani is a specialist of mathematical analysis applied to problems of statistical physics, geometry and probability. His books on gas theory and optimal transport theory have become classics.

Note for Attendees

Join us for coffee and cookies prior to the talk from  2:45pm - 3:00pm : ESB 4133
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MIT
Thu 4 May 2017, 2:00pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Character maps, free loops, and fusion systems
ESB 4133 (PIMS Lounge)
Thu 4 May 2017, 2:00pm-3:00pm

Abstract

A saturated fusion system associated to a finite group G encodes the p-structure of the group as the Sylow p-subgroup enriched with additional conjugation. The fusion system contains just the right amount of algebraic information to for instance reconstruct the p-completion of BG, but not BG itself. Abstract saturated fusion systems F without ambient groups exist, and these have (p-completed) classifying spaces BF as well.

In a joint project with Tomer Schlank and Nat Stapleton, we combine the theory of abstract fusion systems with the work by Hopkins-Kuhn-Ravenel and Stapleton on transchromatic character maps, and we generalize several results from finite groups to fusion systems.

A main ingredient of this project is studying the free loop spaces L(BG) and L(BF) for groups and fusion systems, and constructing transfer maps from L(BG) to L(BH) when H is a subgroup of G.
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Harvard University
Thu 4 May 2017, 3:15pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Nonconnective simplicial commutative rings
ESB 4133 (PIMS Lounge)
Thu 4 May 2017, 3:15pm-4:15pm

Abstract

 Simplicial commutative rings are one of the first steps into "derived" rings that one can take. Many constructions for general E_infty-ring spectra or even Z-algebras are simpler in the world of simplicial commutative rings; however, from a purely homotopy-theoretic or categorical picture they are slightly mysterious. I will explain ongoing work with Bhargav Bhatt on an extended theory of "generalized rings" which extends this category to allow nonconnective objects. Many "equational" constructions which cannot work with E_infty-rings extend well to generalized rings.
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Ecole Normale Supérieure de Lyon
Thu 4 May 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
On the reduction modulo p of crystalline representations of dimension 2
ESB 4127
Thu 4 May 2017, 3:30pm-4:30pm

Abstract

I will talk about the problem of studying the reduction modulo p of crystalline representations of dimension 2 of the Galois group of Q_p. In particular, I will be interested in the following situation: fix Hodge-Tate weights and a residual representation, and consider the locus parametrizing crystalline representations with the given weights and reduction modulo p. What can be said about this locus in general?

(This talk is part of the PIMS focus semester on the mod p Langlands program).
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Cédric Villani
Institut Henri Poincaré
Fri 5 May 2017, 3:00pm
ESB 1013, UBC
PIMS Distinguished Lecture: The best and worst of Henri Poincaré's mistake
ESB 1013, UBC
Fri 5 May 2017, 3:00pm-4:00pm

Details

Abstract: It has been more than hundred years since the death of Henri Poincaré, the world’s greatest mathematician (as we like to say in France, and abroad as well). From the onset, Poincaré’s work and writings, and himself as a universalist and continue to be one of the main symbols of creativity of the human mind and spirit. His errors, however prove that even the greatest, make mistakes.
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ETH Zürich
Fri 5 May 2017, 4:15pm
Number Theory Seminar
Math 126
Elliptic curves over a finite field and traces of Hecke operators
Math 126
Fri 5 May 2017, 4:15pm-5:15pm

Abstract

We consider the set of isomorphism classes of elliptic curves over a finite field k from a probabilistic point of view.  Let t_E denote the trace of the Frobenius endomorphism, A a finite abelian group, 1_A the characteristic function of the event that there is a subgroup of E(k) isomorphic to A, and R a non-negative integer.  In joint work with N. Kaplan we give explicit formulas for the expectation of t_E^R  1_A  in terms of elementary number theory functions and traces of Hecke operators on spaces of classical modular forms.  The formulas are necessarily complicated but quite usable in practice as one knows a lot about these spaces of modular forms.
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Ph.D. Candidate: Dimitrios Roxanas
Mathematics, UBC
Tue 9 May 2017, 12:30pm SPECIAL
Room 202, Anthropology and Sociology Bldg. (ANSOC) 6306 NW Marine Drive, UBC
Long-Time Dynamics for the Energy-Critical Harmonic Map Heat Flow and Nonlinear Heat Equation
Room 202, Anthropology and Sociology Bldg. (ANSOC) 6306 NW Marine Drive, UBC
Tue 9 May 2017, 12:30pm-2:30pm

Details

The emphasis of this thesis is on critical parabolic problems, in particular, the harmonic map heat from the plane to S2, and nonlinear focusing heat equations with an algebraic nonlinearity.

The focus of this work has been on long-time dynamics, stability and singularity formation, and the investigation of the role of special, soliton-like, solutions to the asymptotic behaviour of solutions.

Harmonic Map Heat Flow: We consider m-corotational solutions to the harmonic map heat flow from R2 to S2. We first work in a class of maps with trivial topology and energy of the initial data below two times the energy of the stationary harmonic map solutions. We give a new proof of global existence and decay. The proof is based on the "concentration-compactness plus rigidity" approach of Kenig and Merle and relies on the dissipation of the energy and a profile decomposition. We also treat m-corotational maps (m greater than 4) with non-trivial topology and energy of the initial data less than three times the energy of the stationary harmonic map solutions. Through a new stability argument we rule out finite-time blow-up and show that the global solution asymptotically converges to a harmonic map.

Nonlinear Heat Equation: We also study solutions of the focusing energy-critical nonlinear heat equation. We show that solutions emanating from initial data with energy and kinetic energy below those of the stationary solutions are global and decay to zero. To prove that global solutions dissipate to zero we rely on a refined small data theory, L2-dissipation and an approximation argument. We then follow the "concentration-compactness plus rigidity" roadmap of Kenig and Merle (and in particular the approach taken by Kenig and Koch for Navier-Stokes) to exclude finite-time blow-up.

Note for Attendees

Latecomers will not be admitted.
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Claire Boyer
Theoretical and Applied Statistics Laboratory, Pierre and Marie Curie University
Tue 9 May 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Towards a realistic sampling in compressed sensing (CS)
ESB 4133 (PIMS Lounge)
Tue 9 May 2017, 12:30pm-1:30pm

Abstract

The talk will be divided into 2 parts. First, we will theoretically justify the applicability of compressed sensing (CS) in real-life applications. To do so, I will introduce CS theorems compatible with physical acquisition constraints. These new results do not only encompass structure in the acquisition but also structured sparsity of the signal of interest. Then, we will present a new way to generate subsampling schemes that can be implemented on real sensors and that give good reconstruction results. This work relies on measure projection and will be illustrated in the case of MRI.
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McGill
Thu 11 May 2017, 3:30pm
Number Theory Seminar
ESB 4127
Resonances of hyperbolic surfaces
ESB 4127
Thu 11 May 2017, 3:30pm-4:30pm

Abstract

This is joint work with Frederic Naud (Avignon).  After reviewing general results about resonances on (asymptotically) hyperbolic manifolds, we discuss some recent results on the distribution of resonances for infinite index congruence subgroups of SL(2,Z), as well as some conjectures.
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Université de Montpellier, France
Fri 12 May 2017, 1:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127 (PIMS videoconferencing room)
Prescribing the curvature of hyperbolic convex bodies
ESB 4127 (PIMS videoconferencing room)
Fri 12 May 2017, 1:00pm-2:00pm

Abstract

 The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure \mu , Alexandrov problem consists in proving the existence of a convex body whose curvature measure is \mu . In the Euclidean space, this problem is equivalent to an optimal transport problem on the sphere.
 
In this talk I will consider Alexandrov problem for convex bodies of the hyperbolic space. After defining the curvature measure, I will explain how to relate this problem to a non linear Kantorovich problem on the sphere and how to solve it.
 
Joint work with J\’er\^ome Bertrand.
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Institut de Mathématiques de Jussieu
Mon 15 May 2017, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-adic etale cohomology of p-adic symmetric spaces, Lecture 1
ESB 4127
Mon 15 May 2017, 11:00am-12:00pm

Abstract

We will present different ways to compute the p-adi etale cohomology of layers of the Drinfeld tower, and give applications to the p-adic local Langlands correspondence. (Lecture 1 of 4)

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Boston University
Mon 15 May 2017, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Period maps in p-adic geometry, Lecture 1
ESB 4127
Mon 15 May 2017, 3:30pm-4:30pm

Abstract

On a complex variety, you can integrate a differential form over a cycle to get a period.   For instance, an elliptic curve has two periods, whose quotient gives an element of the upper half plane.  There is a family of concepts (Hodge decomposition, variation of Hodge structures, Shimura varieties) arising from the study of periods on families of complex varieties.  What if the complex variety is replaced with a rigid-analytic variety over a p-adic field?  We will review work of Tate, Fontaine, Kedlaya-Liu, Scholze and others that falls under the domain of p-adic Hodge theory.  One goal will be to understand the surprising Hodge-Tate period map, defined by Scholze, attached to the modular curve at infinite level. (Lecture 1 of 4)

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Institut de Mathématiques de Jussieu
Tue 16 May 2017, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-adic etale cohomology of p-adic symmetric spaces, Lecture 2
ESB 4127
Tue 16 May 2017, 11:00am-12:00pm

Abstract

We will present different ways to compute the p-adi etale cohomology of layers of the Drinfeld tower, and give applications to the p-adic local Langlands correspondence. (Lecture 2 of 4)
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Boston University
Tue 16 May 2017, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Period maps in p-adic geometry, Lecture 2
ESB 4127
Tue 16 May 2017, 3:30pm-4:30pm

Abstract

On a complex variety, you can integrate a differential form over a cycle to get a period.   For instance, an elliptic curve has two periods, whose quotient gives an element of the upper half plane.  There is a family of concepts (Hodge decomposition, variation of Hodge structures, Shimura varieties) arising from the study of periods on families of complex varieties.  What if the complex variety is replaced with a rigid-analytic variety over a p-adic field?  We will review work of Tate, Fontaine, Kedlaya-Liu, Scholze and others that falls under the domain of p-adic Hodge theory.  One goal will be to understand the surprising Hodge-Tate period map, defined by Scholze, attached to the modular curve at infinite level. (Lecture 2 of 4)
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ENS de Lyon
Wed 17 May 2017, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-adic etale cohomology of p-adic symmetric spaces, Lecture 3
ESB 4127
Wed 17 May 2017, 11:00am-12:00pm

Abstract

We will present different ways to compute the p-adi etale cohomology of layers of the Drinfeld tower, and give applications to the p-adic local Langlands correspondence. (Lecture 3 of 4)
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Boston University
Wed 17 May 2017, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Period maps in p-adic geometry, Lecture 3
ESB 4127
Wed 17 May 2017, 3:30pm-4:30pm

Abstract

On a complex variety, you can integrate a differential form over a cycle to get a period.   For instance, an elliptic curve has two periods, whose quotient gives an element of the upper half plane.  There is a family of concepts (Hodge decomposition, variation of Hodge structures, Shimura varieties) arising from the study of periods on families of complex varieties.  What if the complex variety is replaced with a rigid-analytic variety over a p-adic field?  We will review work of Tate, Fontaine, Kedlaya-Liu, Scholze and others that falls under the domain of p-adic Hodge theory.  One goal will be to understand the surprising Hodge-Tate period map, defined by Scholze, attached to the modular curve at infinite level. (Lecture 3 of 4)
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ENS de Lyon
Thu 18 May 2017, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
p-adic etale cohomology of p-adic symmetric spaces, Lecture 4
ESB 4127
Thu 18 May 2017, 11:00am-12:00pm

Abstract

We will present different ways to compute the p-adi etale cohomology of layers of the Drinfeld tower, and give applications to the p-adic local Langlands correspondence. (Lecture 4 of 4)
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UCSD
Thu 18 May 2017, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Multivariate (phi, Gamma)-modules
ESB 4127
Thu 18 May 2017, 3:30pm-4:30pm

Abstract

The classical theory of (phi, Gamma)-modules relates continuous p-adic representations of the Galois group of a p-adic field with modules over a certain mildly noncommutative ring. That ring admits a description in terms of a group algebra over Z_p which is crucial for Colmez's p-adic local Langlands correspondence for GL_2(Q_p). We describe a method for applying a key property of perfectoid spaces, the analytic analogue of Drinfeld's lemma, to the construction of "multivariate (phi, Gamma)-modules" corresponding to p-adic Galois representations in more exotic ways. Based on joint work with Annie Carter and Gergely Zabradi.
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Boston University
Fri 19 May 2017, 11:00am SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Period maps in p-adic geometry, Lecture 4
ESB 4127
Fri 19 May 2017, 11:00am-12:00pm

Abstract

On a complex variety, you can integrate a differential form over a cycle to get a period.   For instance, an elliptic curve has two periods, whose quotient gives an element of the upper half plane.  There is a family of concepts (Hodge decomposition, variation of Hodge structures, Shimura varieties) arising from the study of periods on families of complex varieties.  What if the complex variety is replaced with a rigid-analytic variety over a p-adic field?  We will review work of Tate, Fontaine, Kedlaya-Liu, Scholze and others that falls under the domain of p-adic Hodge theory.  One goal will be to understand the surprising Hodge-Tate period map, defined by Scholze, attached to the modular curve at infinite level. (Lecture 4 of 4)
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University of Toronto
Thu 25 May 2017, 3:30pm SPECIAL
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Ordinary representations and locally analytic socle for GL_n(Q_p)
ESB 4127
Thu 25 May 2017, 3:30pm-4:30pm

Abstract

Suppose that rho is an irreducible automorphic n-dimensional global p-adic Galois representation that is upper-triangular locally at p. In previous work with Breuil we constructed a unitary representation of GL_n(Q_p) on a p-adic Banach space (depending only on rho locally at p) that is an extension of finitely many principal series, and we conjectured that this representation occurs globally in a space of p-adic automorphic forms cut out by rho. In work in progress we prove many new cases of this conjecture, assuming that rho is moreover crystalline with distinct Hodge-Tate weights.
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Yale University
Mon 29 May 2017, 10:30am SPECIAL
Hugh Dempster Pavillion Room 110
The Laplacian Matrices of Graphs: Algorithms and Applications
Hugh Dempster Pavillion Room 110
Mon 29 May 2017, 10:30am-11:30am

Details

The Laplacian matrices of graphs arise in many fields, including Machine
Learning, Computer Vision, Optimization, Computational Science, and of
course Network Analysis.  We will explain what these matrices are and why
they appear in so many applications.

We then survey recent ideas that allow us to solve systems of linear
equations in Laplacian matrices in nearly linear time, emphasizing the
utility of graph sparsification---the approximation of a graph by a sparser
one---and a recent algorithm of Kyng and Sachdeva that uses random sampling
to accelerate Gaussian Elimination.

Note for Attendees

Note location at the Hugh Dempster Pavillion.
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Mon 29 May 2017, 11:15am SPECIAL
MATH 125
Mathematics Grad Reception
MATH 125
Mon 29 May 2017, 11:15am-12:45pm

Details

This is a lunch followed by the awards presentation.
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Yale University
Mon 29 May 2017, 1:00pm SPECIAL
Department Colloquium
Math Annex 1100
Niven Lecture: Using physical metaphors to understanding networks.
Math Annex 1100
Mon 29 May 2017, 1:00pm-2:00pm

Abstract

Networks describe how things are connected, and are ubiquitous in science and society.  Networks can be very concrete, like road networks  connecting cities or networks of wires connecting computers.  They can represent more abstract connections such as friendship on Facebook.  Networks are widely used to model connections between things that have no real connections. For example, Biologists try to understand how cells work by studying networks connecting proteins that interact with each other, and Economists try to understand markets by studying networks connecting institutions that trade with each other.

Questions we ask about a network include "which components of the network are the most important?", "how well do things like information, cars, or disease spread though the network?", and "does the network have a governing structure?".

I will explain how mathematicians address these questions by modeling networks as physical objects, imagining that the connections are springs, electrical resistors, or pipes that carry fluid, and analyzing the resulting systems.

About the Niven Lectures: Ivan Niven was a famous number theorist and expositor; his textbooks have won numerous awards and have been translated into many languages.  They are widely used to this day. Niven was born in Vancouver in 1915, earned his Bachelor's and Master's degrees at UBC in 1934 and 1936 and his Ph.D. at the University of Chicago in 1938. He was a faculty member at the University of Oregon since 1947 until his retirement in 1982. The annual Niven Lecture, held at UBC since 2005, is funded in part through a generous bequest from Ivan and Betty Niven to the UBC Mathematics Department.

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Ailyn Stötzner
Faculty of Mathematics, TU Chemnitz
Tue 30 May 2017, 12:30pm
ESB 4133 (PIMS Lounge)
Optimal Control of Thermoviscoplasticity
ESB 4133 (PIMS Lounge)
Tue 30 May 2017, 12:30pm-1:30pm

Details

Elastoplastic deformations play a tremendous role in industrial forming. Many of these processes happen at non-isothermal conditions. Therefore, the optimization of such problems is of interest not only mathematically but also for applications.

In this talk we will present the analysis of the existence of a global solution of an optimal control problem governed by a thermovisco(elasto)plastic model. We will point out the difficulties arising from the nonlinear coupling of the heat equation with the mechanical part of the model. Finally, we will discuss first numerical results.

The talk is based on joint work with Roland Herzog and Christian Meyer.
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