Mathematics Institute, Utrecht University

Tue 1 Mar 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Dimensionality Reduction and Uncertainty Quantification for Inverse Problems

ESB 4133 (PIMS Lounge)
Tue 1 Mar 2016, 12:30pm1:30pm
Abstract
Many inverse problems in science and engineering involve multiexperiment data and thus require a large number of forward simulations. Dimensionality reduction techniques aim at reducing the number of forward solves by (randomly) subsampling the data. In the special case of (nonlinear) leastsquares estimation, we can interpret this compression of the data as a (lowrank) approximation of the noise covariance matrix. We show that this leads to different design criteria for the subsampling process. Furthermore, the resulting lowrank structure can be exploited when designing matrixfree methods for estimating (properties of) the posterior covariance matrix. Finally, we discuss the possibility of estimating the noise covariance matrix itself.
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Wed 2 Mar 2016, 10:00am
Math Education Research Reading
Math 126

"Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course"

Math 126
Wed 2 Mar 2016, 10:00am11:00am
Abstract
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University of Calgary and PIMS

Wed 2 Mar 2016, 3:00pm
Probability Seminar
ESB 2012

Propagation of high moments for parabolic Anderson model

ESB 2012
Wed 2 Mar 2016, 3:00pm4:00pm
Abstract
The parabolic Anderson model is the heat equation perturbed by a multiplicative noise. In case of Gaussian noise with nontrivial constant initial datum, the nth moment of the solution grows exponentially fast in long term over the whole spatial domain. If the initial datum is localized, the moment grows exponentially only inside a spacetime cone. Outside of the cone, the moment decays exponentially in long term. We will discuss how to specify these cones. The talk is based on a joint work with Jingyu Huang and David Nualart (available on arXiv:1509.00897).
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University of British Columbia

Wed 2 Mar 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

How to get a Calculus named after you

ESB 4133 (PIMS Lounge)
Wed 2 Mar 2016, 3:15pm4:15pm
Abstract
Anyone can have a theorem but only a select few mathematicians have a Calculus named after them! One such is Tom Goodwillie who constructed a theory analogous to differential calculus for functors from spaces to spaces. I will give an introduction to the Goodwillie Calculus and explain why the identity functor has such an interesting "Taylor series".
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McGill University

Thu 3 Mar 2016, 3:30pm
Number Theory Seminar
room IRMACS 10901 (SFU)

Nonabelian Chabauty on higher genus curves

room IRMACS 10901 (SFU)
Thu 3 Mar 2016, 3:30pm4:30pm
Abstract
The recent work of Minhyong Kim provides us with a very general framework for addressing questions of Diophantine finiteness for hyperbolic curves in an effective way. We will discuss some first steps towards making his strategy explicit for certain classes of higher genus curves, resulting in an effective version of Faltings' finiteness theorem. Together with the recent work of Jennifer Balakrishnan and Netan Dogra on bielliptic curves, these form the first examples of higher genus curves for which Kim's programme may be carried out.
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UBC

Fri 4 Mar 2016, 1:00pm
Graduate Student Seminar
Math 225

Randomly improve a cointoss

Math 225
Fri 4 Mar 2016, 1:00pm2:00pm
Abstract
You are Batman and your lover is captured by Twoface! Wanting to break the monotony of his daily routine, instead leaving her fate to a coin, he smugly decides to play the following game with you. He privately writes down two distinct numbers and reveals one to you, and asks ''Is this the bigger of the two?'', assuming that guessing correctly was equally random as flipping a coin. Little does he know that Batman is a trained probabilist and is uniquely ready for such an situation. Not only do you have a plan, you can execute it in such a way that the odds of winning are strictly better than 50/50! You save your lover, Twoface is defeated, you are a champion (at least with some probability better than 50%).
In this talk we will analyze the above problem and two others in the same vein. We will see unexpected uses of probability to determine unlikely solutions to seemingly arbitrary, hopeless situations to beat the odds in a way that is better than a pure guess.
There is no prerequisites for this talk other than a short attention span, a cando attitude, and a hunger for pizza. Knowing what a random variable is won't hurt either, but is not necessary.
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UC Berkeley

Fri 4 Mar 2016, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

PIMS Hugh C. Morris Lecture: Probability, outside the classroom

ESB 2012
Fri 4 Mar 2016, 3:00pm4:00pm
Abstract
Aside from games of chance and a handful of textbook topics (e.g. opinion polls) there is little overlap between the content of an introductory course in mathematical probability and our everyday perception of chance. In this mostly nonmathematical talk I will give some illustrations of the broader scope of probability.
Why do your friends have more friends than you do, on average? How can we judge someone’s ability to assess probabilities of future geopolitical events, where the true probabilities are unknown? Were there unusually many candidates for the 2012 and 2016 Republican Presidential Nominations whose fortunes rose and fell? Why, in a long line at airport security, do you move forward a few paces and then wait half a minute before moving forward again? In what everyday contexts do ordinary people perceive uncertainty/unpredictability in terms of chance?
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UT Austin

Mon 7 Mar 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126

Categorical Harmonic Analysis on Reductive groups

MATH 126
Mon 7 Mar 2016, 3:00pm4:00pm
Abstract
In this talk I will survey some recent and ongoing work of myself and collaborators (David BenZvi, David Nadler, Hendrik Orem), and others, concerning certain topological field theories associated to a complex reductive group G. The basic example of such a theory, assigns the cohomology of the character variety (i.e. moduli of representations of the fundamental group) to a topological surface. To a point, it assigns the categorical group algebra of Dmodules on G. I will discuss various approaches to studying this theory, including work from my thesis on parabolic induction and restriction functors, work in progress with BenZvi and Nadler on a monoidal quantization of the the group scheme of regular centralizers using translation functors on Whittaker modules, and a categorical highest weight theorem with BenZvi, Nadler and Orem. Our work is partly motivated by the "Arithmetic Harmonic Analysis" developed by Hausel, RodriguezVillegas, and Lettalier, to study the cohomology of character and quiver varieties.
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Laura Barton and Greg Martin
UBC

Tue 8 Mar 2016, 5:30pm
room MATH 204

Ally Skills Workshop—UBC Math

room MATH 204
Tue 8 Mar 2016, 5:30pm7:30pm
Details
This workshop is focused on teaching people of all genders how to support women by taking small, simple, everyday actions. It is designed for voluntary participants who already agree that sexism exists, that it should stop, and that they personally would like to help end it. Undergraduates, graduate students, staff, postdocs, and faculty are all welcome. Refreshments will be served to participants.
We encourage people of all genders to attend the workshop. Men are especially encouraged to learn more about effective approaches to supporting women in mathematics. People of other genders are encouraged to share their knowledge and personal experience. Please register in advance, at: http://tinyurl.com/UBCMathASW
Math Ally Skills Workshop
March 8, 2016
5:30pm–7:30pm (signin begins at 5:15pm)
room MATH 204
Facilitated by Laura Barton and Greg Martin
Laura Barton is a third year Bachelor of Computer Science student and member of the Focus on Women in Computer Science committee. She works to be both an ally and a positive role model for minorities in computer science, and believes we all play a part in creating an inclusive, vibrant culture that will benefit everyone.
Greg Martin is a professor in the Mathematics Department at UBC who has been working at being an active ally for several years. He has participated in the AntiViolence Ally and Positive Space programs at UBC, and continues to write regularly about gender in STEM fields, including an academic paper on the underrepresentation of women in mathematics.
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Wed 9 Mar 2016, 10:00am
Math Education Research Reading
Math 126

"A Characterization of Calculus I Final Exams in U.S. Colleges and Universities"

Math 126
Wed 9 Mar 2016, 10:00am11:00am
Abstract
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UBC/PIMS

Thu 10 Mar 2016, 3:30pm
Number Theory Seminar
room MATH 126

Some finiteness results on monogenic orders in arbitrary characteristic

room MATH 126
Thu 10 Mar 2016, 3:30pm4:30pm
Abstract
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University of Toronto

Fri 11 Mar 2016, 3:00pm
Department Colloquium
Math Annex 1100

Monodromy of shift of argument eigenvectors and cactus groups

Math Annex 1100
Fri 11 Mar 2016, 3:00pm4:00pm
Abstract
The classical method of GelfandZetlin constructs bases in representations of gl_n using iterative restriction to smaller gl_k. For any semisimple Lie algebra this can be generalized using eigenvectors for maximal commutative subalgebra of universal envelopping algebras. In this way, we obtain a family of bases for representations of our Lie algebra. This family is parametrized by the moduli space of marked genus 0 real curves. The fundamental group of this moduli space is called the cactus group and thus we obtain an an action of the cactus group on one of these bases. This action of the cactus group matches an action defined combinatorially using crystals.
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UBC

Mon 14 Mar 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126

TBA

MATH 126
Mon 14 Mar 2016, 3:00pm4:00pm
Abstract
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Univ of California, Davis and UBC

Tue 15 Mar 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Levelset methods for convex optimization

ESB 4133 (PIMS Lounge)
Tue 15 Mar 2016, 12:30pm1:30pm
Abstract
Convex optimization problems in a variety of applications have favorable objectives but complicating constraints, and firstorder methods, often needed for large problems, are not immediately applicable. We propose a levelset approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric problems. We describe the theoretical and practical properties of this approach for a range of problems, including lowrank semidefinite optimization, which arise in matrixcompletion applications.
Joint work with A. Aravkin, J. Burke, D. Drusvyatskiy, S. Roy.
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Johns Hopkins University

Tue 15 Mar 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

KAM theory for whiskered tori in Hamiltonian PDEs with applications to illposed ones

ESB 2012
Tue 15 Mar 2016, 3:30pm4:30pm
Abstract
We develop a KAM theory for tori with hyperbolic directions for PDEs coming mainly from fluid dynamics. One of the features of these PDEs is that they are strongly illposed. However, our method allows to construct specific quasiperiodic solutions. The format of the KAM theorem is a posteriori in a sense I will make precise and this allows to use several perturbative expansions to compute approximate solutions.
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Mathematics

Tue 15 Mar 2016, 4:00pm
Discrete Math Seminar
ESB 4127

Combinatorics of Baxter permutations

ESB 4127
Tue 15 Mar 2016, 4:00pm5:00pm
Abstract
Baxter permutations are permutations whose matrix representations correspond to (renormalized) configurations of points given by the intersections (in the unit square [0,1]^2) of two plotted functions y=f(x) and x=g(y). We will review on their rich combinatorial properties and bijective connections,and give some open questions regarding the limit behaviour of random Baxter permutations.
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Wed 16 Mar 2016, 10:00am
Math Education Research Reading
MATH 126

"Teaching methods comparison in a large calculus class"

MATH 126
Wed 16 Mar 2016, 10:00am12:00pm
Abstract
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Harvard University

Thu 17 Mar 2016, 3:30pm
Topology and related seminars
ESB 2012

RotationInvariance in Algebraic KTheory

ESB 2012
Thu 17 Mar 2016, 3:30pm4:30pm
Abstract
Let C be a triangulated category. The Grothendieck group K_0(C) is defined as the abelian group generated by symbols [X], where X is an object of C, moduli the relation [X] = [X'] + [X''] for every exact triangle X' > X > X'' in C.
A simple consequence of this relation is that the double suspension functor X > X[2] induces the identity map from K_0(C) to itself. In this talk, I will explain how this observation can be seen as the shadow of a certain rotationinvariance phenomenon in algebraic Ktheory, and describe the connection of this phenomenon with the theory of "topological Fukaya categories" introduced by Dyckerhoff and Kapranov.
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Guillermo Martinez Dibene
UBC

Fri 18 Mar 2016, 1:00pm
Graduate Student Seminar
Math 225

Two paradoxes in statistics and related topics.

Math 225
Fri 18 Mar 2016, 1:00pm2:00pm
Abstract
I'll talk about the paradoxes of Simpson and of St. Petersburg; both of these arise when all the information in a subject is reduced to the first moment or centre of mass of the probability.
If time permits, I'd like to address several cases in real life events (if possible, recent ones) where such paradoxes are employed to give information about a subject.
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Harvard University

Fri 18 Mar 2016, 3:00pm
SPECIAL
Department Colloquium / PIMS Seminars and PDF Colloquiums
ESB 2012

PIMSUBC Distinguished ColloquiumThe Siegel Mass Formula, Tamagawa Numbers, and Nonabelian Poincare Duality

ESB 2012
Fri 18 Mar 2016, 3:00pm4:00pm
Abstract
Let L be a positive definite lattice. There are only finitely many positive definite lattices L' which are isomorphic to L modulo N for every N > 0: in fact, there is a formula for the number of such lattices, called the Siegel mass formula. In this talk, I'll review the Siegel mass formula and explain how it was reformulated by Weil as a statement about volumes of adelic groups. I'll then describe some joint work with Dennis Gaitsgory on computing these volumes over function fields using ideas from topology: in particular, a nonabelian version of Poincare duality.
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Chemical and Biological Engineering, WisconsinMadison

Mon 21 Mar 2016, 3:00pm
Institute of Applied Mathematics
LSK 460

State Estimation using Moving Horizon Estimation and Particle Filtering

LSK 460
Mon 21 Mar 2016, 3:00pm4:00pm
Abstract
This seminar provides an overview of currently available methods for state estimation of linear, constrained and nonlinear dynamic systems. The seminar begins with a brief overview of the Kalman filter, which is the optimal estimator for a linear dynamic system subject to independent, normally distributed disturbances. Next, alternatives for treating nonlinear and constrained dynamic systems are discussed. Two complementary methods are presented in some detail: moving horizon estimation, which is based on optimization, and particle filtering, which is based on sampling. The advantages and disadvantages of these two approaches are presented. Topics for new research are suggested that address combining the best features of moving horizon estimators and particle filters.
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Western Ontario

Mon 21 Mar 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126

Hall algebras and sheaves on surfaces

MATH 126
Mon 21 Mar 2016, 3:00pm4:00pm
Abstract
Hall algebras play a prominent role in the interactions between algebraic geometry and representation theory. Recently, "refined" versions of them, called Ktheoretic Hall algebras, were introduced by Schiffmann and Vasserot. They have notable connections with the geometric Langlands correspondence, the theory of quantum groups and gauge theories.
In the first part of the talk, I will give an overview of the theory of Hall algebras. In the second part, I will describe some (new) examples of Ktheoretic Hall algebras. These algebras are related to some stacks of a certain kind of sheaves on noncompact surfaces. (Work in progress with Olivier Schiffmann.)
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Mathematics, University of WisconsinMadison

Tue 22 Mar 2016, 12:30pm
Institute of Applied Mathematics
ESB 4133

Sedimentation in viscous fluids: flexible filaments and boundary effects

ESB 4133
Tue 22 Mar 2016, 12:30pm2:00pm
Abstract
The deformation and transport of elastic filaments in viscous fluids play central roles in many biological and technological processes. Compared with the wellstudied case of sedimenting rigid rods, the introduction of filament compliance may cause a significant alteration in the longtime sedimentation orientation and filament geometry. In the weakly flexible regime, a multiplescale asymptotic expansion is used to obtain expressions for filament translations, rotations and shapes which match excellently with full numerical simulations. In the highly flexible regime we show that a filament sedimenting along its long axis is susceptible to a buckling instability. Embedding the analytical results for a single filament into a meanfield theory, we show how flexibility affects a well established concentration instability in a sedimenting suspension. Related topics will make cameo appearances, from a zoology of dynamics of settling bodies near walls to a new traction boundary integral equation for viscous fluidbody interactions.
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Stephanie van Willigenburg
UBC

Tue 22 Mar 2016, 4:00pm
Discrete Math Seminar
ESB 4127

An introduction to quasisymmetric Schur functions

ESB 4127
Tue 22 Mar 2016, 4:00pm5:00pm
Abstract
In algebraic combinatorics a central area of study is Schur functions. These functions were introduced early in the last century with respect to representation theory, and since then have become important in other areas such as quantum physics and algebraic geometry.
These functions also form a basis for the algebra of symmetric functions, which in turn forms a subalgebra of the algebra of quasisymmetric functions that itself impacts areas from category theory to card shuffling. Despite this strong connection, the existence of a natural quasisymmetric refinement of Schur functions was considered unlikely for many years.
In this talk we will meet such a natural refinement of Schur functions, called quasisymmetric Schur functions. Furthermore, we will see how these quasisymmetric Schur functions refine many wellknown Schur function properties, with combinatorics that strongly reflects the classical case including diagrams, walks in the plane, and pattern avoidance in permutations.
This talk will require no prior knowledge of any of the above terms.
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University of Illinois at UrbanaChampaign and University of Zagreb

Wed 23 Mar 2016, 3:00pm
Probability Seminar
ESB 2012

Boundary Harnack principle and Martin boundary at infinity for Feller processes

ESB 2012
Wed 23 Mar 2016, 3:00pm4:00pm
Abstract
A boundary Harnack principle (BHP) was recently proved for Feller processes in metric measure spaces by Bogdan, Kumagai and Kwasnicki. In this talk I will first show how their method can be modified to obtain a BHP at infinity – a result which roughly says that two nonnegative function which are harmonic in an unbounded set decay at the same rate at infinity. With BHP at hand, one can identify the Martin boundary of an unbounded set at infinity with a single Martin boundary point and show that, in case infinity is accessible, this point is minimal. I will also present analogous result for a finite Martin boundary point. The local character of these results implies that minimal thinness of a set at a minimal Martin boundary point is also a local property of that set near the boundary point. (Joint work with P.Kim and R.Song)
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University of British Columbia

Wed 23 Mar 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

The EHP sequence in A¹ algebraic topology

ESB 4133 (PIMS Lounge)
Wed 23 Mar 2016, 3:15pm4:15pm
Abstract
The classical EHP sequence is a partial answer to the question of how far the unit map of the loopsuspension adjunction fails to be a weak equivalence. It can be used to move information from stable to unstable homotopy theory. I will explain why there is an EHP sequence in A^{1} algebraic topology, and some implications this has for the unstable A^{1} homotopy groups of spheres.
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TU Graz

Thu 24 Mar 2016, 3:30pm
Number Theory Seminar
room MATH 126

Computable absolutely normal numbers and discrepancies

room MATH 126
Thu 24 Mar 2016, 3:30pm4:30pm
Abstract
A real number is said to be normal to base b, b≥2 an integer, if in its base b expansion each finite pattern of digits occurs asymptotically with the expected frequency. A real number is called absolutely normal if it is normal to all integer bases b≥2. So far, it remains an open problem to exhibit a natural example of such a number. We present a number of algorithms that compute absolutely normal numbers in the sense that they successively output the digits to a given base of a real number that can be shown to be absolutely normal. We analyze these algorithms with respect to computational complexity and speed of convergence to normality. Furthermore, we adapt one of the algorithms to the more general setting of Pisot numbers as bases and conclude with some open problems.
Joint with Manfred Madritsch and Robert Tichy.
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University of Edinburgh

Tue 29 Mar 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On the well posedness of the periodic fourth order Schrodinger equation in negative Sobolev spaces

ESB 2012
Tue 29 Mar 2016, 3:30pm4:30pm
Abstract
We will discuss the Cauchy problem for the cubic fourth order nonlinear Schrodinger equation (4NLS) on the circle. We first prove nonexistence of solutions to (4NLS) for initial data lying strictly in negative Sobolev spaces, by using the short time Fourier restriction norm method. Then, we focus on the wellposedness issue of the renoramilzed 4NLS (so called the Wick ordered W4NLS). In particular, by performing normal form reductions infinite many times, we prove wellposedness of (W4NLS) in negative Sobolev spaces. This talk is based on a joint work with Tadahiro Oh (University of Edinburgh).
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Wed 30 Mar 2016, 10:00am
Math Education Research Reading
Math 126

"Student perceptions of pedagogy and persistence in calculus"

Math 126
Wed 30 Mar 2016, 10:00am11:00am
Abstract
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Complex Systems Modeling Group at SFU

Wed 30 Mar 2016, 12:00pm
PIMS Seminars and PDF Colloquiums
UBC Robson Square, Room 485

PIMS Vancouver Lunchbox Lecture: Operational Research and the Criminal Justice System

UBC Robson Square, Room 485
Wed 30 Mar 2016, 12:00pm1:00pm
Abstract
The Criminal Justice System is responsible for upholding public safety through the enforcement of laws, the apprehension, prosecution, and judging of suspects, and the administration of community and custodial sentences. It is highly complex, with interactions between police, prosecutors, judges, the court, and correctional services. Effective and efficient administration of justice is important for maintaining public safety.
We present an overview of operational research modeling applied to the Criminal Justice System. Two case studies are considered: a systems dynamics model of the impact of the 2010 impaired driving legislation in British Columbia and a queue network model of the impact of the Truth in Sentencing Act of Canada.
Registration is free and a light lunch will be provided. For more details and to register for this event, please visit http://www.pims.math.ca/industrialevent/160224pllkv .
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Microsoft Research

Wed 30 Mar 2016, 3:00pm
Probability Seminar
ESB 2012

New Results at the Crossroads of Convexity, Learning and Information Theory

ESB 2012
Wed 30 Mar 2016, 3:00pm4:00pm
Abstract
I will present three new results: (i) the Cramer transform of the uniform measure on a convex body is a universal selfconcordant barrier; (ii) projected Langevin Monte Carlo (i.e. discretized reflected Brownian motion with drift) allows to sample from a logconcave measure in polynomial time; and (iii) Thompson sampling combined with a multiscale exploration solves the Bayesian convex bandit problem. The unifying theme in these results is the interplay between concepts from convex geometry, probability theory, learning and information theory.
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UBC

Thu 31 Mar 2016, 3:30pm
Number Theory Seminar
room MATH 126

Some Fermattype equations via the symplectic method

room MATH 126
Thu 31 Mar 2016, 3:30pm4:30pm
Abstract
Wiles' proof of Fermat's Last Theorem gave birth to the "modular method" to attack Diophantine equations. Since then many other equations were solved using generalizations of this method. However, the success of the generalizations relies on a final "contradiction step" which is invisible in the original proof.
In this talk we will recall the modular method and discuss a tool known as "the symplectic argument" that sometimes allows to complete this extra step. We will also discuss some applications to Fermattype equations, in particular, x^{3} + y^{3} = z^{p}.
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Note for Attendees
Pizza and pop will be provided.