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 Events
Ecole Polytechnique Fédérale de Lausanne (EPFL)
Wed 1 Aug 2012, 3:00pm
Probability Seminar
MATH 126
On the homogenization of the heat equation with random coefficients
MATH 126
Wed 1 Aug 2012, 3:00pm-4:00pm

Abstract

We consider the heat equation with random coefficients on Z^d. The randomness of the coefficients models the inhomogeneous nature of the medium where heat propagates. We assume that the distribution of these coefficients is invariant under spatial translations, and has a finite range of dependence. It is known that if a solution to this equation is rescaled diffusively, then it converges to the solution of a heat equation with constant coefficients. In probabilistic terms, this convergence corresponds to the fact that the associated random walk satisfies a central limit theorem. I will present recent progress on the estimation of the speed of this convergence, based on the random walk representation. 
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UBC
Thu 2 Aug 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
A discussion on stabilizers in general position
Math 126
Thu 2 Aug 2012, 11:30am-1:00pm

Abstract

When an algebraic group G acts linearly on a vector space V, the stabilizer subgroup G_x of elements fixing a point x is dependent on x. For example, the stabilizer at zero is all of G. But often there is a Zariski open subset of V on which all of the stabilizers G_x are the same (up to conjugation, and after extending scalars). I will discuss this phenomenon, and some consequences, paying particular attention to base fields of positive characteristic.
 
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Technion
Tue 7 Aug 2012, 11:00am
Probability Seminar
WMAX 216
Probabilistic and Combinatorial Aspects of the Card-Cyclic to Random Insertion Shuffle
WMAX 216
Tue 7 Aug 2012, 11:00am-12:00pm

Abstract

Consider  a permutation  \sigma\in S_n as a deck of cards numbered from 1 to n and laid out in a row,  where \sigma_j denotes the number of the card that is in the j-th position from the left.\rm\ We study some probabilistic and combinatorial aspects of the  shuffle on S_n defined by removing and then randomly reinserting each of the n cards once, with the removal and reinsertion being performed according to the original left to right order of the cards. The novelty here in this nonstandard shuffle is that every card is removed and reinserted exactly once. The bias that remains turns out to be quite strong and possesses some surprising features.
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UBC
Thu 9 Aug 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
On descents of torsors
Math 126
Thu 9 Aug 2012, 11:30am-1:00pm

Abstract

(TBA)
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University of Toronto
Mon 20 Aug 2012, 3:00pm SPECIAL
Department Colloquium
WMAX 110 (PIMS)
[PIMS distinguished lecture] A glimpse into the differential geometry and topology of optimal transportation
WMAX 110 (PIMS)
Mon 20 Aug 2012, 3:00pm-4:00pm

Abstract

The Monge-Kantorovich optimal transportation problem is to pair producers with consumers so as to minimize a given transportation cost. When the producers and consumers are modeled by probability densities on two given manifolds or subdomains, it is interesting to try to understand the structure of the optimal pairing as a subset of the product manifold. This subset may or may not be the graph of a map.

The talk will expose the differential topology and geometry underlying many basic phenomena in optimal transportation.  It surveys questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality.  It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It establishes new connections --- some heuristic and others rigorous ---based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.


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University of Toronto
Wed 22 Aug 2012, 3:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
[PIMS distinguished lecture] Optimal transportation with capacity constraints
WMAX 110 (PIMS)
Wed 22 Aug 2012, 3:00pm-4:00pm

Abstract

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a given cost function. Here we consider a variation of this problem by imposing an upper bound constraining the joint measures, namely: among all joint measures with fixed marginals and dominated by a fixed measure, find the optimal one.  After computing illustrative examples, we given conditions guaranteeing uniqueness of the optimizer and initiate a study of its properties. Based on a preprint arXived with Jonathan Korman.

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University of Toronto
Fri 24 Aug 2012, 3:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
[PIMS distinguished lecture] Multisector matching with cognitive and social skills: a stylized model for education, work and marriage
WMAX 110 (PIMS)
Fri 24 Aug 2012, 3:00pm-4:00pm

Abstract

Economists are interested in studying who matches with whom (and why) in the educational, labour, and marriage sectors.  With Aloysius Siow, Xianwen Shi, and Ronald Wolthoff, we propose a toy model for this process, which is based on the assumption that production in any sector requires completion of two complementary tasks.  Individuals are assumed to have both social and cognitive skills, which can be modified through education, and which determine what they choose to specialize in and with whom they choose to partner.


Our model predicts variable, endogenous, many-to-one matching.  Given a fixed initial distribution of characteristics, the steady state equilibrium of this model is the solution to an (infinite dimensional) linear program, for which we develop a duality theory which exhibits a phase transition depending on the number of students who can be mentored. If this number is two or more, then a continuous distributions of skills leads to formation of a pyramid in the education market with a few gurus having unbounded wage gradients. One preprint is on the arXiv; a sequel is in progress.

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Mon 27 Aug 2012, 10:00am SPECIAL
One Time Event
LSK 200
Graduate Student Orientation followed by Lunch at noon (Math 125)
LSK 200
Mon 27 Aug 2012, 10:00am-1:00pm

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Vincent Chan
Tue 28 Aug 2012, 8:45am SPECIAL
One Time Event
Math 104
TA Training
Math 104
Tue 28 Aug 2012, 8:45am-6:00pm

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University of Munich
Tue 28 Aug 2012, 2:00pm
Algebraic Groups and Related Structures
MATX 1102
A fiber dimension theorem for stacks
MATX 1102
Tue 28 Aug 2012, 2:00pm-3:00pm

Abstract

The well-known fiber dimension theorem in algebraic geometry says that for every morphism f : X -> Y of integral schemes of finite type, the dimension of each nonempty fiber of f is at least dim X - dim Y. We will discuss two analogues of this theorem, where schemes are replaced by algebraic stacks (or categories fibered in groupoids) and dimension is replaced by essential or canonical dimension. These results will be applied in particular to derive new relations between the essential dimension and canonical dimension of group schemes.
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Vincent Chan
Wed 29 Aug 2012, 8:45am SPECIAL
One Time Event
Math 104
TA Training
Math 104
Wed 29 Aug 2012, 8:45am-6:00pm

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Victoria Hoskins
University of Oxford
Wed 29 Aug 2012, 3:00pm
Algebraic Geometry Seminar
GEOG 101
Finite and infinite stratifications
GEOG 101
Wed 29 Aug 2012, 3:00pm-4:00pm

Abstract

In this talk we compare several different stratifications of parameter spaces of sheaves. The starting point is the infinite Yang-Mills stratification of the space of vector bundles on a compact Riemann surface, which is equal to the stratification by Harder-Narasimhan types. We then go on to look at finite stratifications of some quot schemes associated to a certain group action (the geometric invariant theory quotient for this action is a moduli space for sheaves) and relate this to a stratification of the quot scheme by Harder-Narasimhan types. Finally we discuss the limitations of the finite stratifications and how we could instead modify the set up to get infinite stratifications.
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Ben Davison
IMJ at Universite Paris 7
Wed 29 Aug 2012, 4:00pm
Algebraic Geometry Seminar
GEOG 101
Motivic DT invariants of -2 curves
GEOG 101
Wed 29 Aug 2012, 4:00pm-5:00pm

Abstract

-2 curves are a favorite toy of birational geometers working in dimension 3 - they are slightly more complicated cousins of the resolved conifold. In this talk I'll try to give a reasonably self contained introduction to the theory of motivic DT invariants, and integrality, by explaining how this theory plays out in the case of "noncommutative" -2 curves. It turns out that, in common with the noncommutative conifold, the motivic DT partition function for -2 curves have a strikingly nice form, confirming the integrality conjecture in this case.

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Mario Garcia-Armas
UBC
Thu 30 Aug 2012, 11:30am
Algebraic Groups and Related Structures
MATH 126
Torsors in flat topology (student seminar)
MATH 126
Thu 30 Aug 2012, 11:30am-12:30pm

Abstract


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University of Vienna and Schrodinger Institute
Thu 30 Aug 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Sandpiles and the Harmonic Model
Math 126
Thu 30 Aug 2012, 2:00pm-3:00pm

Abstract

 
The critical sandpile model was introduced by Bak, Tang and Wiesenfeld in 1987--88 and attracted a lot of attention after the discovery of a somewhat elusive abelian group structure of the model by Dhar. In this lecture I will try to shed some light on this group property by showing that the sandpile model is an equal entropy symbolic cover of a Z2-action (or, in d dimensions, of a Z^d-action) by automorphisms of a compact abelian group, the 'harmonic model'. The construction involved goes back to Vershik, who used it to define Markov or sofic partitions for hyperbolic toral automorphisms (joint work with Evgeny Verbitskiy).

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