UBC

Wed 3 Apr 2013, 3:00pm
Probability Seminar
ESB 2012

Sublinear resistance on the low dimensional critical branching random walk

ESB 2012
Wed 3 Apr 2013, 3:00pm4:00pm
Abstract
We show that the electric resistance between the origin and the nth generation of a critical oriented branching random walk in dimensions d<6 is at most n^(1a) for some a>0. As a corollary, the spectral dimension of the trace is strictly larger than 4/3 (its value when d>6) answering a question of Barlow, Jarai , Kumagai and Slade.
Joint work with Antal Jarai.
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Thu 4 Apr 2013, 9:00am
SPECIAL
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Thu 4 Apr 2013, 9:00am11:30am
Details
This thesis consists of four chapters and deals with two different problems which are both related to the broad topic of special values of anticyclotomic Lfunctions.
In Chapter 3, we generalize some results of Vatsal on studying the special values of RankinSelberg Lfunctions in an anticyclotomic Zpextension. Let g be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level N over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant D. We study the ladic valuation of the special values L(g,χ,1/2) as χ varies over the ring class characters of K of Ppower conductor, for some fixed prime ideal P. We prove our results under the only assumption that the prime to P part of N is relatively prime to D.
In Chapter 4, we compute a basis for the twodimensional subspace Sk/2(Γ₀(4N),F) of halfintegral weight modular forms associated, via the Shimura correspondence, to a newform F of level N and weight k1, which satisfies L(F,1/2)≠0. Here we let k be a positive integer such that k ≡ 3 mod 4 and N be a positive squarefree odd integer. This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given F via local considerations, once a form in the Kohnen space has been determined. The squares of the Fourier coefficients of these forms are known to be essentially proportional to the central critical values of the Lfunction of F twisted by some quadratic characters.
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Centre de recherches mathématiques  Université de Montréal

Thu 4 Apr 2013, 3:00pm
SPECIAL
Topology and related seminars
ESB 2012

A Short Elementary Survey of Symplectic Topology

ESB 2012
Thu 4 Apr 2013, 3:00pm4:00pm
Abstract
Symplectic topology can be thought as the mathematical versant of String theory: they were born independently at the same time, the second one as a fantastic enterprise to unify largescale and lowscale physics, and the first one to solve classical dynamical problems on periodic orbits of physical problems, the famous Arnold conjectures. In the 80's, Gromov's revolutionary work opened a new perspective by presenting symplectic topology as an almost Kähler geometry (a concept that he defined), and constructing the corresponding theory which is entirely covariant (whereas algebraic geometry is entirely contravariant). A few years later, Floer and Hofer established the bridge between the two interpretations of Symplectic topology, the one as a dynamical theory and the one as a Kähler theory. This bridge was confirmed for the first time by LalondeMcDuff who related explicitly the first theory to the second by showing that Gromov's NonSqueezing Theorem is equivalent to Hofer's energycapacity inequality.
Nowadays, Symplectic Topology is a very vibrant subject, and there is perhaps no other subject that produces new and deep moduli spaces at such a pace ! More recent results will also be presented.
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UBC

Thu 4 Apr 2013, 3:30pm
Number Theory Seminar
room MATH 126

Roth's theorem in the primes

room MATH 126
Thu 4 Apr 2013, 3:30pm4:30pm
Abstract
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Columbia University

Thu 4 Apr 2013, 4:10pm
SPECIAL
Algebraic Geometry Seminar
ESB 2012

Stable pairs and the HOMFLY polynomial

ESB 2012
Thu 4 Apr 2013, 4:10pm5:10pm
Abstract
Given a planar curve singularity, Oblomkov and Shende conjectured a precise relationship between the geometry of its Hilbert scheme of points and the HOMFLY polynomial of the associated link. I will explain a proof of this conjecture, as well as a generalization to colored invariants proposed by Diaconescu, Hua, and Soibelman.
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CNRSIHES

Fri 5 Apr 2013, 3:00pm
SPECIAL
Department Colloquium
ESB 2012 (PIMS) Note the special location

The Work of Misha Gromov, a Truly Original Thinker

ESB 2012 (PIMS) Note the special location
Fri 5 Apr 2013, 3:00pm4:00pm
Abstract
The work of Misha Gromov has revolutionized geometry in many respects, but at the same time introduced a geometric point of view in many questions. His impact is very broad and one can say without exaggeration that many fields are not the same after the introduction of Gromov's ideas.
I will try and explain several avenues that Gromov has been pursuing, stressing the changes in points of view that he brought in non technical terms.
Here is a list of topics that the lecture will touch:
1. The hPrinciple,
2. Distance and Riemannian Geometry,
3. Group Theory and Negative Curvature,
4. Symplectic Geometry,
5. A wealth of Geometric Invariants,
6. Interface with other Sciences,
7. Conceptualizing Concept Creation
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McGill University

Mon 8 Apr 2013, 3:00pm
Harmonic Analysis Seminar
Math 126

Conformal invariants from nodal sets

Math 126
Mon 8 Apr 2013, 3:00pm4:00pm
Abstract
We study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n >=3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n >=3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. This is joint work with Yaiza Canzani, Rod Gover and Raphael Ponge.
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University of Notre Dame

Mon 8 Apr 2013, 3:10pm
Algebraic Geometry Seminar
ESB 4133

Paving Hessenberg Varieties by Affines

ESB 4133
Mon 8 Apr 2013, 3:10pm4:10pm
Abstract
Hessenberg varieties are closed subvarieties of the full flag variety. Examples of Hessenberg varieties include both Springer fibers and the flag variety. In this talk we will show that Hessenberg varieties corresponding to nilpotent elements which are regular in a Levi factor of the Lie algebra are paved by affines. We then provide a partial reduction from paving Hessenberg varieties for arbitrary elements to paving those corresponding to nilpotent elements, generalizing results of Tymoczko.
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UBC

Mon 8 Apr 2013, 4:10pm
Algebraic Geometry Seminar
ESB 4133

Cohomology of Springer Fibres and Springer's Weyl group action via localization

ESB 4133
Mon 8 Apr 2013, 4:10pm4:40pm
Abstract
I will apply Martha Precup's theorem on affine pavings to describe the equivariant cohomology algebras of (regular) Springer fibres in terms of certain Weyl group orbits. This will also yield a simple description of Springer's representation of W on the cohomology of the above Springer fibres.
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Chalmers University of Technology

Wed 10 Apr 2013, 3:00pm
Probability Seminar / Symbolic Dynamics and Ergodic Theory Seminar
ESB 2012

The many faces of the T Tinverse process

ESB 2012
Wed 10 Apr 2013, 3:00pm4:00pm
Abstract
The T Tinverse process or equivalently "random walk in random scenery" is a family of stationary processes that exhibits an amazing amount of behavior. Each random walk yields such a process and as you vary the random walk, you obtain essentially all possible ergodic theoretic behaviors. There is also a phase transition that arises which we can only partially prove. I will give an overview of this area which contains work both old and (somewhat) new.
This work is done jointly with a number of people including Frank den Hollander, Mike Keane and Sebastien Blachere.
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Thu 11 Apr 2013, 9:00am
SPECIAL
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Thu 11 Apr 2013, 9:00am11:30am
Details
Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k 2 and of the same level N, both eigenfunctions of the Hecke operators, and both normalized so that a1 = 1. The main result we seek is
that when E and f are congruent mod a prime p (which may be a prime ideal lying over a rational prime p > 2), the algebraic parts of the special values L(E; ; j) and L(f; ; j) satisfy congruences mod the same prime. On the way to proving the congruence result, we construct the modular symbol attached to an Eisenstein series.
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UBC

Thu 11 Apr 2013, 3:30pm
Number Theory Seminar
room MATH 126

Forms in many variables over the primes

room MATH 126
Thu 11 Apr 2013, 3:30pm4:30pm
Abstract
We study the number of solutions of diophantine equations f(x_{1},...,x_{n})=v when the variables x_{i} are restricted to primes. It has been established by Birch and Schmidt that one has the expected number of integer solutions if f is a homogeneous integral polymomial of sufficiently large rank with respect to its degree. We show that the same phenomenon holds when the variables are restricted to primes, extending the results of Hua for diagonal forms. We illustrate some of the ideas on quadratic forms and discuss some elements of the proof of the general case.
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UIUC

Mon 15 Apr 2013, 3:10pm
Algebraic Geometry Seminar
ESB 4133

Varieties in flag manifolds and their patch ideals

ESB 4133
Mon 15 Apr 2013, 3:10pm4:10pm
Abstract
This talk addresses the problem of how to analyze and discuss singularities of a variety X that "naturally'' sits inside a flag manifold. Our three main examples are Schubert varieties, Richardson varieties and Peterson varieties. The overarching theme is to use combinatorics and commutative algebra to study the "patch ideals", which encode local coordinates and equations of X. Thereby, we obtain formulas and conjectures about X's invariants. We will report on projects with (subsets of) Erik Insko (Florida Gulf Coast U.), Allen Knutson (Cornell), Li Li (Oakland University) and Alexander Woo (U. Idaho).
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INRIA Grenoble, France

Tue 16 Apr 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Exploiting uncontrolled information in nonsmooth optimization methods

ESB 4133
Tue 16 Apr 2013, 12:30pm1:30pm
Abstract
We consider convex nonsmooth optimization problems whose objective function is known through some expensive procedure. For example, this is the case in several problems that arise in electricity production management, where the objective function is itself the result of an optimization subproblem.
In this context, it often exists extra information  cheap but with unknown accuracy  that is not used by the algorithms. In this talk, we present a way to incorporate this coarse information into two classical nonsmooth optimization algorithms: Kelley method and level bundle method. We prove that the resulting methods are convergent and we present numerical illustrations showing that they speed up resolution.
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UIUC

Tue 16 Apr 2013, 2:00pm
Discrete Math Seminar
MATH 126

Jeu de taquin, increasing tableaux, and longest increasing subsequences of words

MATH 126
Tue 16 Apr 2013, 2:00pm3:30pm
Abstract
I will describe a theory of jeu de taquin for increasing tableaux, extending Schutzenberger's work on standard Young tableaux. Our original motivation came from Schubert calculus. However, I'll also describe a specific connection to the study of longest increasing sequences (LIS) of words. This is joint work with Hugh Thomas (U. New Brunswick) and Ofer Zeitouni (U. Minnesota).
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Colorado State University

Thu 18 Apr 2013, 3:00pm
Probability Seminar
ESB 2012

Parameter estimation methods for reflected fractional OrnsteinUhlenbeck processes

ESB 2012
Thu 18 Apr 2013, 3:00pm4:00pm
Abstract
The reflected fractional OrnsteinUhlenbeck (RFOU) process arises as the key approximating process for stochastic flow systems with reneging customers/jobs. Our aim is to statistically estimate the key parameters of the system based on the (partially) observed data. We derive the explicit formulas for the standard and sequential maximum likelihood estimators, and their asymptotic/nonasymptotic properties. Our analysis is based on the fractional Girsanov formulas and fundamental martingales for the fractional Brownian motions.
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Fri 19 Apr 2013, 9:00am
SPECIAL
Graduate Student Center, Room 200

Doctoral Exam

Graduate Student Center, Room 200
Fri 19 Apr 2013, 9:00am11:30am
Details
In Hilbert spaces, five classes of monotone operator of relevance to the theory of monotone operators, variational inequality problems, equilibrium problems, and differential inclusions are investigated. These are the classes of paramonotone, strictly monotone, 3cyclic monotone, 3*monotone (or rectangular, or *monotone), and maximal monotone operators.
Examples of simple operators with all possible combinations of class inclusion are given, which together with some additional results lead to an exhaustive knowledge of monotone class relationships for linear operators, linear relations, and for monotone operators in general.
Many of the example operators considered are the sum of a subdifferential with a skew linear operator (and so are BorweinWiersma decomposable). Since for a single operator its BorweinWiersma decompositions are not unique, clean, essential, extended, and standardized decompositions are defined and the theory developed. In particular, every BorweinWiersma decomposable operator has an essential decomposition, and many sufficient conditions are given for the existence of a clean decomposition.
Various constructive methods are demonstrated together which, given any BorweinWiersma decomposable operator, are able to obtain a decomposition, as long as the operator has starshaped domain. These methods are more accurate if a clean decomposition exists. The techniques used apply a variant of Fitzpatrick's Last Function, the theory of which is developed here, where this function is shown to consist of a Riemann integration and be equivalent to Rockafellar's antiderivative when applied to subdifferentials. Furthermore, a different saddle function representation for monotone operators is created using this function which has theoretical and numerical advantages over more classical representations.
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Tue 23 Apr 2013, 12:30pm
SPECIAL
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Tue 23 Apr 2013, 12:30pm3:00pm
Details
My thesis is dedicated to the study of various spatial stochastic processes from theoretical biology.
For finite interacting particle systems from evolutionary biology, we study two of the simple rules for the evolution of cooperation on finite graph in Ohtsuki, Hauert, Lieberman, and Nowak [Nature 441 (2006) 502505] which were first discovered by clever, but nonrigorous, methods. We resort to the notion of voter model perturbations and give a rigorous proof, very different from the original arguments, that both of the rules of Ohtsuki et al. are valid and are sharp. Moreover, the generality of our method leads to a firstorder approximation for fixation probabilities of general voter model perturbations on finite graphs in terms of the voter model fixation probabilities.
For spatial branching processes from population biology, we prove pathwise nonuniqueness in the stochastic partial differential equation (SPDE) of some onedimensional superBrownian motions with immigration and zero initial value. In contrast to a closely related case studied in a recent work by Mueller, Mytnik, and Perkins, the solutions of the present SPDE are assumed to be nonnegative and are unique in law. In proving possible separation of solutions, we use a novel method, called continuous decomposition, to validate natural immigrantwise semimartingale calculations for the approximating solutions, which may be of independent interest in the study of superprocesses with immigration.
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Yonsei University, Korea

Tue 23 Apr 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in PIMS building)

Green's function for secondorder elliptic and parabolic systems with boundary conditions.

ESB 2012 (in PIMS building)
Tue 23 Apr 2013, 3:30pm4:30pm
Abstract
In this talk, I will describe construction and estimates for Green's function for elliptic and parabolic systems of second order in divergence form subject to various boundary conditions.
Here, we assume minimal regularity assumptions on the coefficients and domains.
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Note for Attendees
Note special day for this seminar.