Swansea University

Mon 5 Jan 2015, 2:30pm
CRG Geometry and Physics Seminar
ESB 4127

Scheme theory in tropical geometry

ESB 4127
Mon 5 Jan 2015, 2:30pm3:30pm
Abstract
In the standard approach to tropicalization, an algebraic subset X of a toric variety over a nonarchimedean valued field k is sent to a weighted polyhedral set Trop(X) which we think of as a combinatorial shadow of X. The result depends only on the kpoints of X. A system of polynomial equations often contains more information than the set of its solutions over a field, and the philosophy of scheme theory is that we should treat the system of equations itself as a fundamental geometric object from which the solution set is derived. Schemetheoretic tropicalization is about realizing Trop(X) as the solution set to an underlying system of polynomial equations over the idempotent semiring of tropical numbers  a system that is constructed in a canonical way from the equations defining X. The theory involves the field with one element, and with these ideas the Berkovich analytification appears as the universal tropicalization of X and as the moduli space of valuations on X.
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Weizmann Institute of Science

Mon 5 Jan 2015, 4:00pm
Department Colloquium
LSK 200

Choice and Chance

LSK 200
Mon 5 Jan 2015, 4:00pm5:00pm
Abstract
A man with a bad memory is given n bins into which he must place n balls, as uniformly as possible. Balls are given to him one at a time, and he must place the ball he has before he receives the next one. If for each ball he randomly chooses the bin, then after adding all n balls the most heavily loaded bin will have around log n/log log n balls. If instead, he chooses two bins at random, and then he places the ball in the less loaded bin, the most loaded bin after n steps will have around log log n balls. When n is large, this represents a dramatic improvement for little extra effort.
This phenomenon is referred to as the 'power of two choices.' In this talk, we will see how the power of two choices survives when we attempt to adapt it to two other settings: preferential attachment graphs and the spacings of randomly distributed points in an interval. In each of these settings, we'll see that adding two choices can have dramatic effects on the behavior of the random processes, though not always in the way one might hope.
Based on joint work with Yury Malyshkin (Tver) and Pascal Maillard (Orsay).
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Swansea

Tue 6 Jan 2015, 12:30pm
Department Colloquium
MATX 1100

Combinatorial models of moduli spaces

MATX 1100
Tue 6 Jan 2015, 12:30pm1:30pm
Abstract
Ribbon graphs provide a powerful combinatorial tool in the study of the moduli space of Riemann surfaces. The theory of quadratic differentials in complex analysis gives a cellular decomposition of the moduli space indexed by ribbon graphs, and this allowed the computation of the Euler characteristic and Kontsevich’s proof of Witten’s intersection number conjecture. Costello found a different ribbon graph model in his work constructing the Bmodel counterpart to GromovWitten theory in terms of topological field theories. In this talk I will review these ideas and describe how to produce Costellotype combinatorial models of moduli spaces of many related classes of objects, such as unoriented, spin and rspin surfaces, surfaces with Gbundles, and 3dimensional handlebodies.
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Weizmann Institute of Science

Tue 6 Jan 2015, 3:30pm
Probability Seminar
MATH 225

Stationary random graphs and the hyperbolic Poisson Voronoi tessellation

MATH 225
Tue 6 Jan 2015, 3:30pm5:00pm
Abstract
We consider the hyperbolic Poisson Voronoi (HPV) tessellation, a triangulation of the hyperbolic plane whose vertices are given by a homogeneous Poisson point process. This triangulation fails to have a positive isoperimetric constant, however we show that it does have a positive "anchored" isoperimetric constant. HPV is an example of a stationary random graph, one which when viewed from the point of view of random walk, has the same law at all times. We review some of the theory of stationary random graphs and give some extensions that allow us to conclude random walk on HPV is ballistic and converges almost surely to a point on the boundary.
This is joint work with Itai Benjamini (Weizmann) and Josh Pfeffer (Harvard).
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Harvard University

Wed 7 Jan 2015, 3:00pm
Department Colloquium
ESB 2012

Renormalisation in statistical mechanics

ESB 2012
Wed 7 Jan 2015, 3:00pm4:00pm
Abstract
The central limit theorem of probability theory asserts under very general assumptions that properly renormalised sums of independent and identically random variables converge to a normal distribution. It can be viewed as a global stability result for a fixed point of a dynamical system. The dynamical system is given by sucessive convolution and the fixed point is the normal distribution. Here independence plays an important role by making the dynamical system autonomous. In statistical mechanics, collections of very strongly dependent random variables are at the heart of many problems. The renormalisation group is a grand extension of the dynamical view of the central limit theorem to systems with strong dependence and spatial structure, in which nontrivial phase portraits arise. I will discuss its background and some applications.
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Harvard University

Thu 8 Jan 2015, 3:30pm
Probability Seminar
MATH 225

Specific heat of 4D spin models

MATH 225
Thu 8 Jan 2015, 3:30pm5:00pm
Abstract
Spin systems generalise the Ising model to spins with a general number of components and general distributions. I will discuss a result with Brydges and Slade on the specific heat of the 4D \varphi^4 model, in which we obtain the precise asymptotic behaviour for the approach of the critical point for a general number of components.
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York University

Fri 9 Jan 2015, 3:00pm
Department Colloquium
LSK 200

Subword Complexes in Combinatorics, Discrete Geometry, and Algebra

LSK 200
Fri 9 Jan 2015, 3:00pm4:00pm
Abstract
Subword complexes are simplicial complexes introduced by A. Knutson and E. Miller as a tool to study Gröbner geometry of Schubert polynomials. In this talk, I will present some relevant results about of these objects in combinatorics, discrete geometry, and algebra. In particular, I will focus on:
 combinatorics of triangulations and multitriangulations of convex polygons,
 two applications in cluster algebras and Hopf algebras, and
 geometric constructions of multiassociahedra.
This talk is based on joint works with Nantel Bergeron, JeanPhilippe Labbé, Vincent Pilaud, and Christian Stump.
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Sat 10 Jan 2015, 9:00am
SPECIAL
MATH 204

Analysis  Qualifying Exams

MATH 204
Sat 10 Jan 2015, 9:00am12:00pm
Details
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Sat 10 Jan 2015, 1:00pm
SPECIAL
MATH 204

Differential Equations  Qualifying Exams

MATH 204
Sat 10 Jan 2015, 1:00pm4:00pm
Details
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Sat 10 Jan 2015, 1:00pm
SPECIAL
MATH 204

Algebra Qualifying Exams

MATH 204
Sat 10 Jan 2015, 1:00pm4:00pm
Details
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Mon 12 Jan 2015, 1:00pm
Math Education Research Reading
MATHX1118

An evaluative Calculus Project: applying Bloom's taxonomy to the Calculus Classroom

MATHX1118
Mon 12 Jan 2015, 1:00pm2:00pm
Abstract
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Northwestern University

Mon 12 Jan 2015, 3:10pm
CRG Geometry and Physics Seminar
ESB4127

Functorial axioms for Heisenbergpicture quantum field theory

ESB4127
Mon 12 Jan 2015, 3:10pm4:10pm
Abstract
The usual AtiyahSegal "functorial" description of quantum field theory corresponds to the "Schrodinger picture" in quantum mechanics. I will describe a slight modification that corresponds to the "Heisenberg picture", which I will argue is better physically motivated. The example I am most interested in is a version of quantum ChernSimons theory that does not require the level to be quantized; it provides a neat packaging of pretty much all objects of skein theory.
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UT Austin

Mon 12 Jan 2015, 4:00pm
Department Colloquium
LSK 200

Some phase transitions in the stochastic block model

LSK 200
Mon 12 Jan 2015, 4:00pm5:00pm
Abstract
The stochastic block model is a random graph model that was originally introduced 30 years ago tomodel community structure in networks. To generate a random graph from this model, begin with two classes of vertices and then connect each pair of vertices independently at random, with probability p if they are in the same class and probability q otherwise. Some questions come to mind: can we reconstruct the classes if we only observe the graph? What if we only want to partially reconstruct the classes? How different is this model from an ErdosRenyi graph anyway? The answers to these questions depend on p and q, and we will say exactly how.
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McGill University

Tue 13 Jan 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

The multiplier method of constructing conservative finite difference schemes for differential equations

ESB 4133 (PIMS Lounge)
Tue 13 Jan 2015, 12:30pm1:30pm
Abstract
Structurepreserving discretizations are numerical methods which can preserve important structures of differential equations at the discrete level. For systems with a Hamiltonian or variational structure, geometric integrators such as symplectic and variational integrators are a class of discretizations that can preserve symplectic structure, first integral, phase space volume or symmetry at the discrete level. In this talk, we present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. The proposed discretization is shown to be consistent for any order of accuracy and that by construction, the discrete densities can be exactly conserved. In particular, the multiplier method does not require the system to possess a Hamiltonian or variational structure. Examples, including dissipative problems, are given to illustrate the method. This is joint work with Alexander Bihlo at Memorial University and JeanChristophe Nave at McGill University.
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UT Austin

Tue 13 Jan 2015, 3:30pm
Probability Seminar
MATH 225

Gaussian noise stability

MATH 225
Tue 13 Jan 2015, 3:30pm5:00pm
Abstract
Given two correlated Gaussian vectors, X and Y, the noise stability of a set A is the probability that both X and Y fall in A. In 1985, C. Borell proved that halfspaces maximize the noise stability among all sets of a given Gaussian measure. We will give a new, and simpler, proof of this fact, along with some extensions and applications. Specifically, we will discuss hitting times for the OrnsteinUhlenbeck process, and a noisy Gaussian analogue of the "double bubble" problem.
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Brown University

Tue 13 Jan 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Recent gluing constructions in Differential Geometry

ESB 2012
Tue 13 Jan 2015, 3:30pm4:30pm
Abstract
I will first discuss doubling and desingularization constructions for minimal surfaces and applications on closed minimal surfaces in the round spheres, free boundary minimal surfaces in the unit ball, and selfshrinkers for the Mean Curvature flow. In the final part of the talk I will discuss my collaboration with Simon Brendle on constructions for Einstein metrics on fourmanifolds and related geometric objects.
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U. Texas, Austin

Wed 14 Jan 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

Random Subdivisions & Neural Coding

ESB 2012 (PIMS)
Wed 14 Jan 2015, 3:00pm4:00pm
Abstract
In the first part, I will talk about random subdivisions obtained from projections of polytopes. These are related to random polytopes and zeros of random tropical polynomials. In the second part, I will discuss results and open problems in neural coding, with emphasis on decoding grid cells.
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Stanford University

Thu 15 Jan 2015, 1:00pm
Probability Seminar
MATX 1100

A two scale proof of the EyringKramers formula

MATX 1100
Thu 15 Jan 2015, 1:00pm2:00pm
Abstract
A two scale proof of the EyringKramers formula
(joint work with Andre Schlichting)
We consider a driftdiffusion process on a smooth potential landscape with small noise. We give a new proof of the EyringKramers formula which asymptotically characterizes the spectral gap of the generator of the diffusion. The proof is based on a refinement of the twoscale approach introduced by Grunewald, Otto, Villani, and Westdickenberg and of the meandifference estimate introduced by Chafai and Malrieu. The new proof exploits the idea that the process has two natural timescales: a fast timescale resulting from the fast convergence to a metastable state, and a slow timescale resulting from exponentially long waiting times of jumps between metastable states. A nice feature of the argument is that it can be used to deduce an asymptotic formula for the logSobolev constant, which was previously unknown.
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Harvard University

Thu 15 Jan 2015, 3:30pm
Number Theory Seminar
room MATH 126

Local character expansion, hyperelliptic curves, and endoscopy

room MATH 126
Thu 15 Jan 2015, 3:30pm4:30pm
Abstract
An admissible representation of a reductive padic group has its character as a distribution on the group, invariant under conjugation. The asymptotic behavior of the character is given by socalled HarishChandra–Howe local character expansion, which expressed the character near the identity in terms of a finite linear combination (of Fourier transforms of nilpotent orbital integrals). In this talk, we show examples about how the coefficients in this expansion arise as the numbers of rational points on varieties over the residue field, which will be certain covers of hyperelliptic curves in our example. We also talk about how the endoscopy transfer identity appears as geometric identities regarding the first cohomology of these curves.
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Stanford University

Fri 16 Jan 2015, 3:00pm
Department Colloquium
LSK 200

The logSobolev inequality for unbounded spin systems

LSK 200
Fri 16 Jan 2015, 3:00pm4:00pm
Abstract
The logSobolev inequality (LSI) is a very useful tool for analyzing highdimensional situations. For example, the LSI can be used for deriving hydrodynamic limits, for estimating the error in stochastic homogenization, for deducing upper bounds on the mixing times of Markov chains, and even in the proof of the Poincaré conjecture by Perelman. For most applications, it is crucial that the constant in the LSI is uniform in the size of the underlying system. In this talk, we discuss when to expect a uniform LSI in the setting of unbounded spin systems. We will also explain a connection to the KLS conjecture.
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Mon 19 Jan 2015, 1:00pm
Math Education Research Reading
MATX1118

“When good teaching leads to bad results: the disasters of “welltaught” mathematics courses” by Alan H. Schoenfeld

MATX1118
Mon 19 Jan 2015, 1:00pm2:00pm
Abstract
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Institute of Computational Science, Universita della Svizzera italiana

Mon 19 Jan 2015, 3:00pm
SPECIAL
Institute of Applied Mathematics
LSK 460

Performance Engineering of Seismic Simulations for Future Exascale Architectures

LSK 460
Mon 19 Jan 2015, 3:00pm4:00pm
Abstract
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UBC

Mon 19 Jan 2015, 3:00pm
Harmonic Analysis Seminar
Math 204

Discrete Fourier restriction theorems in two dimensions

Math 204
Mon 19 Jan 2015, 3:00pm4:00pm
Abstract
Consider the plane with the discrete topology. A function belongs to its Fourier algebra if and only if that function is equal to the convolution of two squaresummable functions. Call such a product weak on a set if its restriction to that set is squaresummable. We show that weakness on the interior of a strictly convex subset of the plane implies weakness on the boundary of that subset. Here the words "interior" and "boundary" refer to the usual notions in the usual topology on the plane. We also show that weakness on the boundary follows from weakness on the interior of the complement of a strictly convex set in the plane. That is essentially due to V.A. Yudin, via a dual method. Our methods here are direct and visual.
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MIT

Mon 19 Jan 2015, 4:00pm
Department Colloquium
LSK 200

Grid Ramsey problem and related questions

LSK 200
Mon 19 Jan 2015, 4:00pm5:00pm
Abstract
The HalesJewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated result of Shelah from 1988 gives a significantly improved bound for this theorem. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. Hoping to further improve Shelah's result, more than twenty years ago, Graham, Rothschild and Spencer asked whether there exists a polynoimal bound for this lemma. In this talk, we present the answer to their question and discuss numerous connections of the cube lemma with other problems in Ramsey theory.
Joint work with David Conlon (Oxford), Jacob Fox (MIT), and Benny Sudakov (ETH Zurich)
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Institute of Computational Science, Universita della Svizzera Italiana

Tue 20 Jan 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Direct solvers for sparse matrices: Introduction, applications and supercomputing

ESB 4133 (PIMS Lounge)
Tue 20 Jan 2015, 12:30pm1:30pm
Abstract
We will review the stateofthe art techniques in the parallel direct solution of linear systems of equations and present several recent new research directions. This includes (i) fast methods for evaluating certain selected elements of a matrix function that can be used for solving the KohnShamequation without explicit diagonalization and (ii) stochastic optimization problems under uncertainty from power grid problems from electrical power grid systems. Several algorithmic and performance engineering advances are discussed to sove the underlying sparse linear algebra problems. The new developments include novel incomplete augmented multicore sparse factorizations, multicore and GPUbased dense matrix implementations, and communicationavoiding Krylov solvers. We also improve the interprocess communication on Cray systems to solve e.g. 24hour horizon power grid problems from electrical power grid systems of realistic size with up to 1.95 billion decision variables and 1.94 billion constraints. Fullscale results are reported on Cray XC30 and BG/Q, where we observe very good parallel efficiencies and solution times within a operationally defined time interval. To our knowledge, "realtime"compatible performance on a broad range of architectures for this class of problems has not been possible prior to present work.
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SFU

Thu 22 Jan 2015, 3:30pm
Number Theory Seminar
room MATH 126

The proportion of nonordinary hyperelliptic curves

room MATH 126
Thu 22 Jan 2015, 3:30pm4:30pm
Abstract
An elliptic curve in characteristic p is either ordinary or supersingular, depending on whether or not it has points of order p. It is known that elliptic curves are typically ordinary, and also exactly how many are supersingular for each prime p. However, for higher genus curves little is known. In this talk, we will discuss several higher genus generalizations of supersingular elliptic curves, focussing on the hyperelliptic case. In particular we discuss recent heuristics, computational results, and theorems on the proportion of hyperelliptic curves that are nonordinary.
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Beijing Institute of Technology

Thu 22 Jan 2015, 4:30pm
Symmetries and Differential Equations Seminar
Math 126

Symmetry analysis and conservation laws for fractional order partial differential equations

Math 126
Thu 22 Jan 2015, 4:30pm5:30pm
Abstract
In this talk, we consider symmetries and conservation laws of FPDEs equation with RiemannLiouville derivatives. First, we briefly review Lie group methods and the construction of conservation laws for PDEs. Within the framework of Lie group theory, we extend Lie group analysis to solve problems involving FPDEs. Finally, we give some examples to illustrate applications of the methods. Some open questions will be discussed.
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MIT

Fri 23 Jan 2015, 3:00pm
Department Colloquium
LSK 200

Algebraic Ktheory and categorification

LSK 200
Fri 23 Jan 2015, 3:00pm4:00pm
Abstract
Algebraic Ktheory is a subtle and remarkable invariant of rings (as well as more general objects). In this talk, I will describe recent advances that demonstrate that it is the natural stable homotopy theory of higher categories, and I will explain how this description provides new approaches both to structures on algebraic Ktheory and to an important web of conjectures of Waldhausen, Hopkins, and Rognes.
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Mon 26 Jan 2015, 1:00pm
Math Education Research Reading
MATX1118

"Student learning and perceptions in a flipped linear algebra course" by Betty Love, Angie Hodgea, Neal Grandgenettb & Andrew W. Swifta

MATX1118
Mon 26 Jan 2015, 1:00pm2:00pm
Abstract
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DWAVE

Mon 26 Jan 2015, 3:00pm
Institute of Applied Mathematics
LSK 460

Quantum computation: from DWAVE to sheaves

LSK 460
Mon 26 Jan 2015, 3:00pm4:00pm
Abstract
I start with DWAVE, a successful BC company building and selling quantum computers. I go through the math, the chip and the controversies. I explain how one can program DWAVE machines and solve NP hard problems. I then talk about measurement based quantum computation (MBQC, also a BC product), lots of math, no controversies but no machines. I explain how it relates to Einstein–Podolsky–Rosen paradox and topos theory.
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Stanford University

Mon 26 Jan 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127

Picard Groups of K3 Moduli Spaces

ESB 4127
Mon 26 Jan 2015, 3:00pm4:00pm
Abstract
Polarized K3 surfaces of genus g can be thought of as families of canonical curves. As such, their moduli space K_g has similar properties to M_g. For instance, both are unirational for low values of g, and both have discrete Picard group. In this talk, we will use the explicit unirationality of K_g to compute its Picard number in a few cases, which verifies the NoetherLefschetz conjecture for genus up to 10.
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UBC

Mon 26 Jan 2015, 4:00pm
Department Colloquium
LSK 200

Azumaya Algebras and Obstruction Theory

LSK 200
Mon 26 Jan 2015, 4:00pm5:00pm
Abstract
Azumaya Algebras are a generalization of central simple algebras over fields, and have been studied since the 1950s. In this talk, I shall explain how topological obstruction theory for PGLn bundles can be used to answer questions about Azumaya Algebras over rings.
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Oxford Mathematical Institute

Thu 29 Jan 2015, 12:30pm
Department Colloquium
MATX 1100

Stable and Consistent Algorithms for Numerical Computation on Curved Surfaces

MATX 1100
Thu 29 Jan 2015, 12:30pm2:00pm
Abstract
The Closest Point Method is a set of mathematical principles and associated numerical techniques for solving partial differential equations (PDEs) posed on curved surfaces or other general domains. The method works by embedding the surface in a higherdimensional space and solving the PDE in that space using simple finite difference and interpolation schemes.
This presentation outlines how a chance encounter with instability improved our understanding of the method and is leading to new formulations with proven convergence properties.
We will also briefly survey some applications in thinfilm flows, reactiondiffusion equations, bulksurface coupling, point clouds, and image processing.
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U. of Pennsylvania

Thu 29 Jan 2015, 3:30pm
Probability Seminar
MATH 104

Harnack inequalities for degenerate diffusions

MATH 104
Thu 29 Jan 2015, 3:30pm5:00pm
Abstract
Abstract: We will present probabilistic and analytic properties of a class of degenerate diffusion operators arising in population genetics, the socalled generalized Kimura diffusion operators. Such processes arise as models for the evolution of gene frequencies. We will start by highlighting the main questions of interest and the mathematical difficulties in addressing them. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with singular lowerorder coefficients, and the proof of the scaleinvariant Harnack inequality for nonnegative solutions to the Kimura parabolic equation. The stochastic representation of solutions that we establish is a considerable generalization of the classical results on FeynmanKac formulas concerning the assumptions on the degeneracy of the diffusion matrix, the boundedness of the drift coefficients, and on the a priori regularity of the weak solutions.
This is joint work with Charles Epstein.
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SFU

Thu 29 Jan 2015, 3:30pm
Number Theory Seminar
room ASB 10940 (SFU  IRMACS)

Genus 2 curves with (3, 3)isogenies and 3torsion in Sha

room ASB 10940 (SFU  IRMACS)
Thu 29 Jan 2015, 3:30pm4:30pm
Abstract
We parametrize genus 2 curves with a maximal isotropic (Z/3)^{2} in their Jacobian, together with an explicit description of the associated isogeny. This allows us to perform (3, 3)isogeny descent on various simple principally polarized abelian surfaces and exhibit nontrivial 3part in their TateShafarevich groups. This is joint work with Victor Flynn and Damiano Testa.
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University of Pennsylvania

Fri 30 Jan 2015, 3:00pm
Department Colloquium
LSK 200

The fractional Laplacian operator and its gradient perturbations

LSK 200
Fri 30 Jan 2015, 3:00pm4:00pm
Abstract
The fractional Laplacian operator plays the same paradigmatic role in the theory of nonlocal operators that the Laplacian plays in the theory of local operators. We will present regularity results for solutions to problems defined by the fractional Laplacian operator with gradient perturbations. Our main results are the regularity of solutions in Sobolev spaces to the linear equation in the supercritical regime, when the operator is not elliptic, and the optimal regularity of solutions to the stationary obstacle problem in the supercritical regime.
This is joint work with Charles Epstein and Arshak Petrosyan.
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Note for Attendees
The seminar will start at 2:30, rather than the usual 3pm, in order to avoid a conflict with the 4pm colloquium.Tea will be served at 2:15.