
Sat 1 Sep 2012, 9:00am
SPECIAL
One Time Event
Math 100

Qualifying Exams  Analysis

Math 100
Sat 1 Sep 2012, 9:00am12:00pm
Details
Lunch will be provided only if you are writing the Analysis exam. Lunch is served 12:001:00 pm in Math 125.
If you have food allergies, please let Lee know.
hide


Sat 1 Sep 2012, 1:00pm
SPECIAL
One Time Event
Math 100

Qualifying exams  Differential Equations

Math 100
Sat 1 Sep 2012, 1:00pm4:00pm
Details
hide


Sat 1 Sep 2012, 1:00pm
SPECIAL
One Time Event
Math 100

Qualifying exams  Algebra

Math 100
Sat 1 Sep 2012, 1:00pm4:00pm
Details
hide

UBC

Wed 5 Sep 2012, 3:00pm
Probability Seminar
ESB 2012

Finite range decomposition of Gaussian fields

ESB 2012
Wed 5 Sep 2012, 3:00pm4:00pm
Abstract
I will show a simple method to decompose the Gaussian free field associated to a (weighted) graph or manifold into a sum of finite range Gaussian fields, which are fields that are smoother than the original field and have spatially localized correlations.
hide

UBC

Thu 6 Sep 2012, 11:30am
Algebraic Groups and Related Structures
Math 126

Three counterexamples in the theory of torsors for algebraic groups in characteristic p (Student Seminar)

Math 126
Thu 6 Sep 2012, 11:30am1:00pm
Abstract
We consider three counterexample: A nonsmooth group which has a fppftorsor that is not étale, similarly for a formally smooth group. We also consider how to differentiate between free and nonfree actions for µ_p.
hide

University of North Carolina

Thu 6 Sep 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126

Ergodic and chaotic properties of some noninvertible maps on smooth surfaces

Math 126
Thu 6 Sep 2012, 2:00pm3:00pm
Abstract
We construct noninvertible maps on every compact surface, and study their chaotic properties from both the measure theoretic and topological points of view (joint work with Jane Hawkins).
hide

University of Sussex

Thu 6 Sep 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

Blowup of critical Besov norms at a NavierStokes singularity

ESB 2012 (in the new PIMS building)
Thu 6 Sep 2012, 3:30pm4:30pm
Abstract
In this talk we describe a generalization of the result of EscauriazaSereginSverak on blowup of the L^3 norm at a NavierStokes singularity by establishing the blowup of any weaker critical Besov norm with finite third index as well. Following previous joint works with C. Kenig and with I. Gallagher and F. Planchon respectively, we use the "dispersivetype" method of concentration compactness and critical elements developed by C. Kenig and F. Merle. Joint work with I. Gallagher and F. Planchon
hide

UBC

Fri 7 Sep 2012, 3:00pm
Department Colloquium
MATX 1100

Some recent progress on optimal transport maps

MATX 1100
Fri 7 Sep 2012, 3:00pm4:00pm
Abstract
In this talk, I would like to discuss some recent progress in analysis and geometry of optimal transport maps that arise when mass distributions are matched in most cost efficient way. Especially, continuity of optimal maps will be addressed, which is related to nonlinear partial differential equations as well as Riemannian geometry.
hide

UBC

Mon 10 Sep 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

Trilinear forms and Chern classes of CalabiYau threefolds

ESB 2012
Mon 10 Sep 2012, 3:00pm4:00pm
Abstract
Let X be a CalabiYau threefold. We study the symmetric trilinear form on the integral second cohomology group of X defined by the cup product. Our study is motivated by C.P.C. Wall's classification theorem, which roughly says that the diffeomorphism class of a spin sixfold is determined by the trilinear form. We investigate the interplay between the Chern classes and the trilinear form of X, and demonstrate some numerical relations between them. If time permits, we also discuss some properties of the associated cubic form. This talk is based on a joint work with P.H.M. Wilson.
hide

UBC

Wed 12 Sep 2012, 3:00pm
Probability Seminar
ESB 2012

Volume growth and stochastic completeness of graphs

ESB 2012
Wed 12 Sep 2012, 3:00pm4:00pm
Abstract
We analyze stochastic completeness, or nonexplosiveness, of the variablespeed
random walk (VSRW) on weighted graphs. We prove a criterion relating volume
growth in an adapted metric to stochastic completeness of the VSRW. This
criterion is analogous to the optimal result for Riemannian manifolds and is
shown to be sharp. The proof is accomplished through the construction of a
Brownian motion on a metric graph which behaves similarly to the VSRW under
consideration. Results of Sturm on stochastic completeness for local Dirichlet
spaces are then applicable to this Brownian motion, and nonexplosiveness of
the Brownian motion is shown to imply nonexplosiveness of the VSRW.
hide

UBC

Wed 12 Sep 2012, 3:15pm
Topology and related seminars
PIMS Lounge, ESB 4133

A Duality Theorem for Quotient Stacks with respect to Morava Ktheory

PIMS Lounge, ESB 4133
Wed 12 Sep 2012, 3:15pm4:15pm
Abstract
It was a result of Greenlees and Sadofsky that classifying spaces of finite groups satisfy a Morava Ktheory version of Poincare duality, which was proved by showing the contractibility of the corresponding Tate spectrum. In this series of two talks, I will explain the proof, discuss its generalization to quotient orbifolds and consequences with examples. Some background in equivariant stable homotopy theory will be given. If time permits, I will also explain why the duality map can be viewed as coming from a SpanierWhitehead type construction for differentiable stacks.
hide

UBC

Thu 13 Sep 2012, 11:30am
Algebraic Groups and Related Structures
Math 126

On a counterexample that H^1_fppf(S,X) classifies torsors.

Math 126
Thu 13 Sep 2012, 11:30am1:00pm
Abstract
We will discuss some results concerning the representability of torsors. In the case of an abelian scheme, we will explain how the properties "X is representable" and "the class of X in the first cohomology group is torsion" are related. This will lead us to the construction of an fppf sheaf torsor which is not representable.
hide

UBC

Thu 13 Sep 2012, 3:00pm
Number Theory Seminar
room MATH 126

Dimensions of spaces of cusp forms and newforms

room MATH 126
Thu 13 Sep 2012, 3:00pm4:00pm
Abstract
A formula for the dimension of the space of cuspidal modular forms on Γ_{0}(N) of even weight k≥2 has been known for several decades. More recent but still wellknown is the AtkinLehner decomposition of this space of cusp forms into subspaces corresponding to newforms on Γ_{0}(d) of weight k, as d runs over the divisors of N. A recursive algorithm for computing the dimensions of these spaces of newforms follows from the combination of these two results, but it is desirable to have a formula in closed form for these dimensions. In this talk we describe such a closedform formula, not only for these dimensions, but also for the corresponding dimensions of spaces of newforms on Γ_{1}(N) of weight k≥2. This formula is much more amenable to analysis and to computation. For example, we derive asymptotically sharp upper and lower bounds for these dimensions, and we compute their average orders. We also establish sharp inequalities for the special case of weight2 newforms on Γ_{0}(N), and we report on computations of these dimensions. For example, we can find the complete list of all N such that the dimension of the space of weight2 newforms on Γ_{0}(N) is less than or equal to 100; previous such results had only gone up to 3.
hide

UBC

Fri 14 Sep 2012, 3:00pm
Department Colloquium
MATX 1100

An extremal eigenvalue problem and minimal surfaces in the ball

MATX 1100
Fri 14 Sep 2012, 3:00pm4:00pm
Abstract
Beginning with the work of J. Hersch for the two sphere and that of P. Li and S. T. Yau for more general surfaces, the question of determining surfaces of fixed area that maximize the first eigenvalue has been actively studied. In this talk I will describe recent work with R. Schoen concerning extremal eigenvalue questions for surfaces with boundary. In both cases the eigenvalue problems are related to minimal surface questions. For closed surfaces these are minimal surfaces in spheres while for surfaces with boundary they are related to minimal surfaces in the ball satisfying a natural boundary condition. I will describe some results on determining optimal surfaces. I will also describe some recent work with Martin Li on compactness of the space of free boundary minimal surfaces with a fixed topological type.
hide

University of Michigan

Mon 17 Sep 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

The Gerby GopakumarMarinoVafa Formula

ESB 2012
Mon 17 Sep 2012, 3:00pm4:00pm
Abstract
The GopakumarMarinoVafa formula, proven almost ten years ago, evaluates certain triple Hodge integrals on moduli spaces of curves in terms of Schur functions. It has since been realized that the GMV formula is a special case of the GromovWitten/DonaldsonThomas correspondence for CalabiYau threefolds.
In this talk, I will introduce an orbifold generalization of the GMV formula which evaluates certain abelian Hodge integrals in terms of loop Schur functions. I will introduce local Z_n gerbes over the projective line and show how the gerby GMV formula can be used to prove the GW/DT correspondence for this class of orbifolds. With the remaining time, I will sketch the main ideas in the proof of the formula and discuss generalizations to other geometries.
hide

Math Dept, UBC

Mon 17 Sep 2012, 3:00pm
Institute of Applied Mathematics
LSK 460

Moving Contact Lines: from Giant Slip on Textured Substrates to Water Striders

LSK 460
Mon 17 Sep 2012, 3:00pm4:00pm
Abstract
A threephase contact line forms when a gasliquid interface intersects a solid substrate, and a moving contact line presents a wellknown singularity that cannot be computed using the conventional NavierStokes formalism. I will discuss the use of a diffuseinterface model for computing moving contact lines. The CahnHilliard diffusion is known to regularize the singularity and makes possible a continuumlevel computation. But relating the results to physical reality is subtle. I will show numerical results that suggest a welldefined sharpinterface limit, with a finite contact line speed that can be related to measurements. Then I will discuss applications including enhanced slip on textured substrates and propulsion of water striders on the airwater interface.
hide

UBC

Mon 17 Sep 2012, 3:00pm
Harmonic Analysis Seminar
Math 126

Large scale patterns in sets of positive density of R^n

Math 126
Mon 17 Sep 2012, 3:00pm3:50pm
Abstract
Abstract: It is by now a classical result that sets of positive density of R^2 contain all large distances. It was however observed by Bourgain that the analogue result does not hold for 3 term progressions (3 equally spaced points along a line) in any dimensions. Our aim is to discuss an approach to show that such results are still possible if one changes the metric, for example using the l^4 metric. If time permits we'll mention other possible point configurations. This is ongoing joint work with Brian Cook and Malabika Pramanik.
hide

CS, UBC

Tue 18 Sep 2012, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Semidefinite Optimization, Euclidean Distance Matrices, and Combinatorial Optimization

ESB 4133
Tue 18 Sep 2012, 12:30pm1:30pm
Abstract
During the last two decades, semidefinite optimization has grown into a significant field of research with applications in many diverse areas such as graph theory, distance geometry, combinatorial optimization, lowrank matrix completion, and polynomial optimization. In this talk, I will discuss my work in two of these areas, namely distance geometry and combinatorial optimization.
In distance geometry, Euclidean distance matrices (EDMs) have recently received revived interest due to their use in modern applications such as sensor network localization, protein structure determination, and machine learning. The second reason for this revived interest is the fact that we now have semidefinite optimization solvers that we can use to solve problems involving EDMs (however, we are limited in the size of problems we can solve efficiently due to the high complexity of these semidefinite solvers). I will discuss my theoretical contribution relating cliques in the graph of a partial EDM to identifying a reduced problem formulation, and how I used this result to develop numerical methods to solve largescale instances in each of the three modern applications mentioned above.
In combinatorial optimization, semidefinite optimization is used to efficiently compute highquality bounds to many difficult (in fact, NPhard) problems, such as MaxCut and binary quadratic optimization. This has led to the development of stateoftheart branchandbound methods for solving such problems to optimality. I will discuss my work on a bounding procedure for MaxCut which has been obtained by adding a regularization term to the standard semidefinite bound — this allows us to use basic numerical tools (a eigenvalue decomposition method, and a quasiNewton optimization method) to compute highquality semidefinite bounds efficiently. I will show how this new bounding procedure gives a significant improvement over the current stateoftheart method.

hide

IAM, UBC

Tue 18 Sep 2012, 3:00pm
Stochastic Dynamics Working Group
IAM Lounge

Delayed Negative Feedback: A WarmUp

IAM Lounge
Tue 18 Sep 2012, 3:00pm4:00pm
Abstract
We will discuss a chapter of a book on Delay differential equations by Hal Smith. This chapter can be downloaded from the internet at the following link provided. The chapter is called "Delayed Negative Feedback: A warmup", and it will introduce some of the basics of delay differential equations and how to obtain some analytical results about their stability.
hide

UBC

Tue 18 Sep 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

NonUniqueness Phenomena for the 3D Euler Equations

ESB 2012 (in the new PIMS building)
Tue 18 Sep 2012, 3:30pm4:30pm
Abstract
Since the famous work of V. Scheffer about 20 years ago, it has been known that the Cauchy problem for the incompressible Euler equations has nonunique weak solutions. Recently, De Lellis and Szekelyhidi demonstrated that this phenomenon can be viewed as an instance of the socalled hprinciple, thereby providing a shorter and more general proof of the nonuniqueness. In this talk I will briefly review their method and then present some subsequent results, including global existence and nonuniqueness for 3D Euler, the approximation of measurevalued solutions by weak ones, and nonuniqueness for shear flow initial data.
hide

UBC

Wed 19 Sep 2012, 3:00pm
Probability Seminar
ESB 2012

On the supercritical phase of interlacement percolation

ESB 2012
Wed 19 Sep 2012, 3:00pm4:00pm
Abstract
The random interlacements (at level u) is a one parameter family of random subsets of Z^d (d>=3), introduced recently by A.S. Sznitman, which arises as the
local limit of the trace of a simple random walk on a ddimensional torus, when the size of the torus goes to infinity. The parameter u controls the density of
the interlacement. The vacant set at level u (i.e. the complement set of the random interlacement at level u) undergoes nontrivial percolation phase transition
as u varies. We study the supercritical phase and show that finite connected components of the vacant set are "small" for all d>=3 if u is small enough. Our
method is markedly different from that of A. Teixeira (2011), which gives the analogous result for d>=5.
hide

University of Iowa

Wed 19 Sep 2012, 3:15pm
Topology and related seminars
PIMS Lounge, ESB 4133

Open book foliation and fractional Dehn twist coefficient

PIMS Lounge, ESB 4133
Wed 19 Sep 2012, 3:15pm4:15pm
Abstract
This is joint work with Tetsuya Ito. Fractional Dehn twist coefficient (FDTC), defined by HondaKazezMatic, is an invariant of mapping classes. In this talk we study FDTC by using open book foliation method, then obtain results in topology, geometry, and contact geometry of the openbookmanifold of a mapping class.
hide

Stanford University

Thu 20 Sep 2012, 3:30pm
Number Theory Seminar
room ESB 2012 (PIMS)

Pseudoreductive groups

room ESB 2012 (PIMS)
Thu 20 Sep 2012, 3:30pm4:30pm
Abstract
The theory of reductive groups has many applications in number theory, geometry, and representation theory. For some purposes it is natural to consider a more general notion of "pseudoreductive" group, first studied by Borel & Tits. We will explain the motivation for this (with examples), and discuss the structure theory that has been established in recent years, and mention some applications. If time permits, we'll discuss some more recent developments. This is joint work with O. Gabber and G. Prasad.
hide

UBC

Mon 24 Sep 2012, 3:00pm
Algebraic Geometry Seminar
ESB 2012

Essential Dimension and ErrorCorrecting Codes

ESB 2012
Mon 24 Sep 2012, 3:00pm4:00pm
Abstract
Let p be a prime, r >= 3, and n_i = p^{a_i} for positive integers a_1,...,a_r. Set G = GL_{n_1} x ... x GL_{n_r}, and let \mu be a central subgroup of G. The Galois cohomology set H^1(K, G/\mu) classifies rtuples of central simple algebras satisfying linear equations in the Brauer group Br(K). We study the essential dimension of G/\mu by constructing the 'code' associated to /mu.
hide

UBC

Tue 25 Sep 2012, 3:00pm
SPECIAL
Topology and related seminars
ESB 4127

A Duality Theorem for Quotient Stacks with respect to Morava Ktheory, Part II

ESB 4127
Tue 25 Sep 2012, 3:00pm4:00pm
Abstract
This is the continuation of my previous talk.
It was a result of Greenlees and Sadofsky that classifying spaces of finite groups satisfy a Morava Ktheory version of Poincare duality, which was proved by showing the contractibility of the corresponding Tate spectrum. In this series of two talks, I will explain the proof, discuss its generalization to quotient orbifolds and consequences with examples. Some background in equivariant stable homotopy theory will be given. If time permits, I will also explain why the duality map can be viewed as coming from a SpanierWhitehead type construction for differentiable stacks.
hide

UBC

Tue 25 Sep 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

Regularity for solutions of non local parabolic equations

ESB 2012 (in the new PIMS building)
Tue 25 Sep 2012, 3:30pm4:30pm
Abstract
We study the regularity of solutions of parabolic equations of the form
u_t  Iu = f,
where I is a fully non linear non local operator. We prove C^\alpha regularity in space and time and, under different assumptions on the kernels,
C^{1,\alpha}; in space for translation invariant equations. The proofs rely on a weak parabolic ABP and the classic ideas of K. Tso and L. Wang. Our results remain uniform as \sigma goes to 2 allowing us to recover most of the regularity results of the local case.
This is a joint work with H ector Chang Lara.
hide

UBC

Tue 25 Sep 2012, 4:00pm
Algebraic Groups and Related Structures
MATX 1102

A quick Introduction to Chow Groups and Motives

MATX 1102
Tue 25 Sep 2012, 4:00pm5:00pm
Abstract
We will explain the basic definitions of Chow groups, correspondences and Chow motives. This will be the first talk in a series to help us study the incompressibility of certain varieties.
hide

UBC

Wed 26 Sep 2012, 2:00pm
Undergraduate Colloquium
MATX 1102

Topological Data Analysis

MATX 1102
Wed 26 Sep 2012, 2:00pm3:00pm
Abstract
UBC/UMC is the Undergraduate Mathematics Colloquium at UBC.
These talks are for undergraduates interested in mathematics and mathematical research. They are put on by professors, senior graduate students and visitors to the department. Graduate students are also invited to attend.
Title: Topological Data Analysis
Abstract: This is not an applied math talk. On the contrary: I will show how the abstract tools of Algebraic Topology can be used to assemble lowdimensional representations of data into highdimensional structures. An example of such an assembly would be the brain's inference of a 3D environment from a 2D image from each eye.
hide

University of Cambridge

Wed 26 Sep 2012, 3:00pm
SPECIAL
Department Colloquium
Earth Sciences Bldg (ESB) Room 2012

On the SylvesterGallai Theorem (PIMS/UBC Distinguished Colloquium)

Earth Sciences Bldg (ESB) Room 2012
Wed 26 Sep 2012, 3:00pm4:00pm
Abstract
The SylvesterGallai Theorem states that, given any set P of n points in the plane not all on one line, there is at leads one line through precisely two points of P. Such a line is called an ordinary line. How many ordinary lines must there be? The SylvesterGallai Theorem says that there must be at leads one but, in recent joint work with T. Tao, we have shown that there must be at least n/2 if n is even and at least 3n/4  C if n is odd, provided that n is sufficiently large. These results are sharp. My plan in the talk is to give an overview of this problem and of our work towards its solution.
hide

École Polytechnique Fédérale de Lausanne

Thu 27 Sep 2012, 3:30pm
Number Theory Seminar
room ESB 2012 (PIMS)

Upper bounds for Euclidean minima

room ESB 2012 (PIMS)
Thu 27 Sep 2012, 3:30pm4:30pm
Abstract
The Euclidean division is a basic tool when dealing with the ordinary integers. It does not extend to rings of integers of algebraic number fields in general. It is natural to ask how to measure the "deviation" from the Euclidean property, and this leads to the notion of Euclidean minimum. The case of totally real number fields is of special interest, in particular because of a conjectured upper bound (conjecture attributed to Minkowski). The talk will present some recent results, obtained jointly with Piotr Maciak.
hide

Ecole Polytechnique Fédérale de Lausanne

Fri 28 Sep 2012, 3:00pm
SPECIAL
Department Colloquium
MATH ANNEX 1100

Quadratic forms and finite groups (PIMS/UBC Distinguished Colloquium)

MATH ANNEX 1100
Fri 28 Sep 2012, 3:00pm4:00pm
Abstract
The study of quadratic forms is a classical and important topic of algebra and number theory. A natural example is the trace form of a finite Galois extension. This form has the additional property of being invariant under the Galois group, leading to the notion of "selfdual nornal basis", introduced by Lenstra. The aim of this talk is to give a survey of this area, and to present some recent joint results with Parimala and Serre.
hide

Note for Attendees
Refreshments will be served in MATH 125 at 2:45 pm before the colloquium.