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 Events
UBC
Tue 1 Feb 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Picard Group
Math 126
Tue 1 Feb 2011, 11:30am-12:30pm

Abstract

We define the Picard group of a variety using (Weil) divisors and show that the Picard group of projective space P^n is the integers. We also describe the two generators of the Picard group of P^n as line bundles. (A continuation of last week's talk)
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University of Nice
Tue 1 Feb 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110
The Heat Flow as gradient flow
WMAX 110
Tue 1 Feb 2011, 3:30pm-4:30pm

Abstract

Aim of the talk is to make a survey on some recent results concerning analysis over spaces with Ricci curvature bounded from below. I will show that the heat flow in such setting can be equivalently built either as gradient flow of the natural Dirichlet energy in L^2 or as gradient flow if the relative entropy in the Wasserstein space. I will also show how such identification can lead to interesting analytic and geometric insights on the structures of the spaces themselves. From a collaboration with L.Ambrosio and G.Savare'.
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UBC
Tue 1 Feb 2011, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
Jannsen's Theorem on Numerical Equivalence and Semi-Simplicity I
MATX 1102
Tue 1 Feb 2011, 3:30pm-4:30pm

Abstract

In Sujatha's talk in this seminar last semester, several equivalence relations (numerical equivalence, homological equivalence and algebraic equivalence)
appeared along with Jannsen's theorem that the category of motives is abelian semi-simple if and only if the equivalence relation is numerical equivalence.   The proof of this theorem is beautiful, simple and short.  (The main tool is the double-centralizer theorem.) I will try to do it justice in my lectures.

 
 
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UBC
Tue 1 Feb 2011, 4:00pm
Discrete Math Seminar
Math 126
Digraphs are 2-weight choosable
Math 126
Tue 1 Feb 2011, 4:00pm-5:00pm

Abstract

An edge-weighting vertex colouring of a (di)graph is an edge-weight
assignment such that the accumulated weights at the vertices yields
a proper vertex colouring. If such an assignment from a set S exists,
we say the graph is S-weight colourable. Using the Combinatorial 
Nullstellensatz and a classical theorem of Schur, we show that every
digraph is S-weight colourable for any set S of size 2. It is 
conjectured that every graph with no isolated edge is {1,2,3}-weight
colourable. We explore the problem of classifying those graphs which
are {1,2}-weight colourable. 

This is joint work with Reza Naserasr, Mike Newman, Ben Seamone, 
and Brett Stevens.  
 
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University of Victoria
Wed 2 Feb 2011, 4:00pm
Topology and related seminars
WMAX 110
A homology theory for hyperbolic dynamical systems
WMAX 110
Wed 2 Feb 2011, 4:00pm-5:00pm

Abstract

As part of Smale's program for smooth dynamics, David Ruelle gave a definition of a Smale space as (roughly) a topological dynamical system which has a local product structure of contracting and expanding directions for the dynamics. A special case is certain symbolic dynamical systems called shifts of finite type. In the late 1970's, Wolfgang Krieger, motivated by ideas from C*-algebra theory and K-theory, provided a beautiful algebraic invariant for shifts of finite type. The aim of this talk is to show how this invariant may be extended to the class of all Smale spaces as a kind of homology theory which provides a Lefschetz formula. Such a theory was conjectured by Bowen. (I will attempt to define and give examples of all the dynamical concepts: Smale space, shifts of finite type, etc.)
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MIT
Thu 3 Feb 2011, 3:30pm SPECIAL
Discrete Math Seminar
Math 126
Triangulations of root polytopes and Kirillov's conjectures
Math 126
Thu 3 Feb 2011, 3:30pm-4:30pm

Abstract

A type A_{n-1} root polytope is the convex hull in R^n of the origin and a subset of the points e_i-e_j, 1\leq i< j \leq n. A collection of triangulations of these polytopes can be described by reduced forms of monomials in an algebra generated by n^2 variables x_{ij}, for 1\leq i< j \leq n. In a closely related noncommutative algebra, the reduced forms of monomials are unique, and correspond to shellable triangulations whose simplices are indexed by noncrossing alternating trees. Using these triangulations we compute Ehrhart polynomials of a family of root polytopes. We extend the above results to more general families of polytopes and algebras of types C_n and D_n. Special cases of our results prove several conjectures of Kirillov regarding these algebras.
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Michael Schraudner
CMM - Universidad de Chile
Thu 3 Feb 2011, 4:40pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Factor maps onto and extensions of Z^d full shifts
Math 126
Thu 3 Feb 2011, 4:40pm-6:00pm

Abstract

 
While in the theory of one-dimensional subshifts we have a fairly complete picture about when a factor map between two shifts of finite type exist. The situation for Z^d shifts of finite type is much more complicated and so far even the case of factoring onto the full Z^d shift has only a partial answer (which we will present in the talk).
Moreover we will introduce a class of Z^d matrix shifts whose entropy is constructed to be exactly log N and which come with a natural factor map onto the corresponding full N shift. We will give some examples of those equal-entropy extensions of Z^d full shifts realizing various mixing and periodic point conditions.
This will be a rather informal talk on some things I am working on and some related open questions. 
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MIT
Fri 4 Feb 2011, 3:00pm
Department Colloquium
MATX 1100
Branched polymers and hyperplane arrangements
MATX 1100
Fri 4 Feb 2011, 3:00pm-4:00pm

Abstract

Branched polymers are certain configurations of nonoverlapping disks in the plane.  In 2003 Brydges and Imbie discovered some remarkable formulas for the volumes of configuration spaces of branched polymers.  These formulas mysteriously involve combinatorial numbers like (n-1)!.  We introduce branched polymers arising from any central hyperplane arrangement A and express the volume of the resulting configuration space through the characteristic polynomial of A.  This is joint work with Alex Postnikov.
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UBC
Mon 7 Feb 2011, 10:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Sheaves on the étale site
Math 126
Mon 7 Feb 2011, 10:30am-12:00pm

Abstract

We describe Galois covers in the context of the étale site of a scheme, seen as a generalization of Galois field extensions. In particular, we use this idea to show that the étale cohomology of a field agrees with the standard galois cohomology.
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Stanford University
Mon 7 Feb 2011, 3:00pm
Algebraic Geometry Seminar
WMAX 110
The Hilbert stack
WMAX 110
Mon 7 Feb 2011, 3:00pm-4:00pm

Abstract

The Hilbert scheme of projective space is a fundamental moduli space in algebraic geometry. The naive generalization of the Hilbert scheme can fail to exist for some spaces of interest, however. D. Rydh and I have generalized the Hilbert scheme, to the Hilbert stack, and have shown that the Hilbert stack is always algebraic. I will describe the Hilbert stack and some of the ideas behind the proof.
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George Bluman
Math UBC
Mon 7 Feb 2011, 3:00pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Nonlocally related systems II
Math Annex 1118
Mon 7 Feb 2011, 3:00pm-4:00pm

Abstract

We will continue with a historical development of the construction and uses of nonlocally related systems as well as open problems. 
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Mon 7 Feb 2011, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
Mon 7 Feb 2011, 3:30pm-4:30pm

Abstract


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Mario Garcia Armas
UBC
Tue 8 Feb 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Galois algebras
Math 126
Tue 8 Feb 2011, 11:30am-1:00pm

Abstract

We describe galois algebras as torsors of finite groups. Thus giving a description of H^1(k,G), in the case that G is a finite group.
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Colin Clark
UBC (emeritus)
Tue 8 Feb 2011, 2:00pm
Mathematical Biology Seminar
WMAX 110
Ocean-atmosphere coupling and the likelihood of doom
WMAX 110
Tue 8 Feb 2011, 2:00pm-3:00pm

Abstract


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UBC
Tue 8 Feb 2011, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
Jannsen's Theorem on Numerical Equivalence and Semi-Simplicity II
MATX 1102
Tue 8 Feb 2011, 3:30pm-4:30pm

Abstract

In Sujatha's talk in this seminar last semester, several equivalence relations (numerical equivalence, homological equivalence and algebraic equivalence) appeared along with Jannsen's theorem that the category of motives is abelian semi-simple if and only if the equivalence relation is numerical equivalence.   The proof of this theorem is beautiful, simple and short.  (The main tool is the double-centralizer theorem.) I will try to do it justice in my lectures.
 
 
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UBC
Tue 8 Feb 2011, 4:00pm
Discrete Math Seminar
Math 126
A census of one-factorizations of the complete 3-uniform hypergraph of order 9
Math 126
Tue 8 Feb 2011, 4:00pm-5:00pm

Abstract

The one-factorizations of the complete 3-uniform hypergraph with 9 vertices are classified by means of an exhaustive computer search. It is shown that the number of isomorphism classes of such one-factorizations is 103000.
 
This is joint work with Patric Ostergard.
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UBC
Wed 9 Feb 2011, 3:00pm
Undergraduate Colloquium
MATH 105
Viscous Fingering in Porous Media: Modelling Unstable Growth Processes
MATH 105
Wed 9 Feb 2011, 3:00pm-4:00pm

Abstract

We're pleased to have Bud Homsy back to give a UBC/UMC talk.

Title: Viscous Fingering in Porous Media: Modelling Unstable Growth Processes

Q:
What do oil production, fractal aggregates, electrochemical deposition, and lightening have in common?

A: The underlying mathematics, of course!

This talk will focus on modeling unstable flow in porous media, which important in enhanced oil production. It is also a good example of unstable growth processes and of free boundary problems in mathematics. I’ll start by reviewing the basic partial differential equations of fluid flow in porous materials and then discuss the stability analysis of the uniform flow state, with some emphasis on physical mechanisms. Then I’ll discuss the nonlinear regime of this instability which is only accessible through numerical simulation. This will help understand the connection between this instability and other unstable growth processes.
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Hyun Jae Yoo
Hankyong National University
Wed 9 Feb 2011, 4:00pm
Probability Seminar
MATH 126
Determinantal point processes: Gibbianness and dynamics
MATH 126
Wed 9 Feb 2011, 4:00pm-5:00pm

Abstract

Determinantal (also called fermion) point processes are point processes  (on discrete or continuous spaces)  whose  correlation functions are given by determinants of matrices coming from certain kernel functions. In this talk we start with a couple of examples where DPP's appear. Focusing on the discrete DPP's, we discuss the Gibbianness of them. We benefit from this property to construct some dynamics that leave a DPP invariant. We will typically construct Glauber and Kawasaki dynamics for DPP's.
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Guillermo Mantilla-Soler
UBC
Thu 10 Feb 2011, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Mordell-Weil ranks in towers of modular Jacobians
Room WMAX 216 (PIMS - UBC Campus)
Thu 10 Feb 2011, 3:00pm-3:50pm

Abstract

Please see attached abstract.

Note for Attendees

Refreshments will be served between the two talks.
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University of Alabama at Birmingham
Thu 10 Feb 2011, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
PIMS
Zero-velocity Lieb-Robinson bounds in the disordered xy-spin chain
PIMS
Thu 10 Feb 2011, 3:30pm-4:30pm

Abstract

The well understood phenomenon of Anderson localization says (in its dynamical formulation) that adding random fluctuations to the potential of a Schrodinger operator will lead to the absence of wave transport for the solution of the time-dependent Schrodinger equation. Several years ago it was argued by Burrell and Osborne that a corresponding phenomenon should hold in quantum spin systems. As an example they used the xy-spin chain to show on the physical level of rigor that the introduction of disorder will lead to zero-velocity Lieb-Robinson bounds. We will show
how recent results on Anderson localization can be used to make this result rigorous and, in fact, to improve on the conclusions reached by Burrell and Osborne.
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Doug Lind
University of Washington
Thu 10 Feb 2011, 3:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Periodic Points and Entropy
Math 126
Thu 10 Feb 2011, 3:30pm-5:00pm

Abstract

There is a general principle for algebraic dynamical systems 
that the growth rate of periodic points should be the entropy.
This has to be suitably interpreted, and I will formulate a 
conjecture for which there are no known counterexamples. For
a single toral automorphism this is equivalent to a deep
result in diophantine analysis. For several commuting group
automorphisms the corresponding diophantine result is not 
known, but I will describe recent work with Schmidt and 
Verbitskiy using homoclinic points which provides an 
alternative approach in many cases.
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PIMS/SFU/UBC
Thu 10 Feb 2011, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
The Mahler measures of algebraic numbers with rational product
Room WMAX 216 (PIMS - UBC Campus)
Thu 10 Feb 2011, 4:10pm-5:00pm

Abstract

Let x be an algebraic number and let M(x) denote its Mahler measure.  If x = x1...xN the t-metric
Mahler measure Mt(x) is a convenient way to study the smallest possible values of M(xn) in
terms of x.  In joint work with J. Jankauskas, we resolve an earlier conjecture 
regarding Mt(x) for rational x.  This result suggests a generalization to higher degree x,
which turns out, however, to be false.  We provide an infinite family of quadratic
counterexamples and discuss how the conjecture should be modified.
 
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University of Alabama at Birmingham
Fri 11 Feb 2011, 3:00pm
Department Colloquium
MATX 1100
Bubbles tend to the boundary
MATX 1100
Fri 11 Feb 2011, 3:00pm-4:00pm

Abstract

Consider the negative Dirichlet or Neumann Laplacian on a square. Add a potential perturbation
which is supported on a small disk. How should the potential be placed in the square in order
to minimize the lowest eigenvalue of the resulting Schrodinger operator? The answer to this
question for the case of Neumann conditions is very different from the answer for the
Dirichlet case. In particular, for the Neumann case the answer is independent of the
sign of the potential. We will discuss how the solution of this problem ultimately
led to a proof of localization near the spectral boundary of the random displacement
model. The latter is a model for a random Schrodinger operator which is used to
model structural disorder in a crystal. A proof of localization for this model was long
considered challenging due to the non-monotone dependence of the operator on the random parameters.
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UBC
Mon 14 Feb 2011, 11:00am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) The category of sheaves on a site
Math 126
Mon 14 Feb 2011, 11:00am-12:30pm

Abstract

We continue to describe sheaves of abelian groups on an arbitrary étale site. In particular, we prove that the category has enough injective; allowing us to define étale sheaf cohomology. 
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Athena Nguyen
UBC
Mon 14 Feb 2011, 2:00pm
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Cech cohomology
Math 126
Mon 14 Feb 2011, 2:00pm-3:30pm

Abstract

As in most cohomology theories over a topological space, calculations can be tricky. To solve this problem, we talk about Cech cohomology on an étale site, and show the equivalence of this cohomology to the étale cohomology whenever the base space satisfies some mild conditions.
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UBC
Tue 15 Feb 2011, 11:00am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Algebraic groups on étale sites
Math 126
Tue 15 Feb 2011, 11:00am-12:30pm

Abstract

I will talk about the sheaf associated to a group scheme, focusing on the case of the multiplicative group. I will discuss connections between its cohomology and the Picard and Brauer groups of a scheme.
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UBC
Tue 15 Feb 2011, 2:00pm
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Universal division Algebras
Math 126
Tue 15 Feb 2011, 2:00pm-3:30pm

Abstract

This is the first of a series of talks in which, subject to time and interests, we will discuss some or all of the following:
-Definitions and basic results from the theory of Polynomial Identity (PI) rings.
-Major results from PI-theory: The Amitsur-Levitzki Theorem, Kaplansky’s Theorem, Posner’s Theorem.
-Construction of the ring of generic matrices and the universal division algebra.
-The centre of the universal division algebra.
-“Universal” properties of the universal division algebra: Galois subfields and rational specialization.
-The universal division algebra is an object of maximal essential dimension.
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Mario Garcia Armas
UBC
Mon 21 Feb 2011, 10:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Calculations in the étale cohomology
Math 126
Mon 21 Feb 2011, 10:30am-12:00pm

Abstract

 We continue on with the study of H^1(X_et, G) and its interpretation the set of principal homogenous spaces for G, when G is a sheaf of groups on X_et.
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Alexander Volberg
Michigan State University
Mon 21 Feb 2011, 3:00pm
Harmonic Analysis Seminar
MATH 126
Random zeros of analytic functions and random tiling of complex plane
MATH 126
Mon 21 Feb 2011, 3:00pm-4:00pm

Abstract

 
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University of Strasbourg/PIMS
Mon 21 Feb 2011, 4:30pm
Topology and related seminars
WMAX 110
Working seminar in Topology
WMAX 110
Mon 21 Feb 2011, 4:30pm-5:30pm

Abstract

This is a continuation on the topic of cyclic homology
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UBC
Tue 22 Feb 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Universal Divison Algebras
Math 126
Tue 22 Feb 2011, 11:30am-1:00pm

Abstract

This is the second of a series of talks in which we will discuss some of the following:
-Major results from PI-theory: The Amitsur-Levitzki Theorem, Kaplansky’s Theorem, Posner’s Theorem.
-Construction of the ring of generic matrices and the universal division algebra.
-The centre of the universal division algebra.
-“Universal” properties of the universal division algebra: Galois subfields and rational specialization.
-The universal division algebra is an object of maximal essential dimension.
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Rachel Kuske
Department of Mathematics, UBC
Tue 22 Feb 2011, 3:15pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)
The Fokker-Planck Equation
IAM Lounge (LSK 306)
Tue 22 Feb 2011, 3:15pm-4:15pm

Abstract


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UBC
Wed 23 Feb 2011, 4:00pm
Topology and related seminars
WMAX 110
Equivariant K-theory and maximal rank subgroups
WMAX 110
Wed 23 Feb 2011, 4:00pm-5:00pm

Abstract

Let G be a compact connected Lie group act on a topological space X
in such a way that all isotropy subgroups are connected and of maximal
rank. In this talk we provide a criterion to determine when K_{G}^{*}(X) is
free over the representation ring R(G).
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UBC
Wed 23 Feb 2011, 4:00pm
Probability Seminar
MATH 126
Branched polymers and Mayer expansions I
MATH 126
Wed 23 Feb 2011, 4:00pm-5:00pm

Abstract

The Mayer expansion is a power series expansion that has a central
place in statistical mechanics. It is also full of combinatorial miracles that
relate it to graphs, forests and branched polymers. I will discuss the background,
the results, and some open problems.

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Lunch Series for Teaching and Learning
Thu 24 Feb 2011, 12:30pm
One Time Event
MATH 126
Student Perceptions of Mathematics
MATH 126
Thu 24 Feb 2011, 12:30pm-1:30pm

Details

Do your students (or other people you meet) say anything about math or learning math that makes you cringe?

Student perceptions of mathematics play a role in their motivation and approaches to learning in their math courses. Last term, we adapted an existing survey for Physics (*) and surveyed students at the beginning and end of a range of Math courses (including several first-year calculus courses). This has allowed us to assess student attitudes and perceptions, and to track how they shift over time.

In this Lunch Series, we will present our development of the survey and some of these initial results. We would also like to gather input from members of the department about the content of the survey: what perceptions or attitudes do mathematicians have about their own subject, and which would you hope students develop as they pursue their undergraduate degree? We hope to see you there for discussion and pizza.
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Tom Meyerovich
PIMS-UBC
Thu 24 Feb 2011, 2:00pm
PIMS Seminars and PDF Colloquiums
WMAX 110
On measures of maximal entropy for subshifts
WMAX 110
Thu 24 Feb 2011, 2:00pm-3:00pm

Abstract

Entropy" is a key notion in the study in of dynamical systems. This quantity reflects the "uncertainty", or "randomness" of a system. Subshifts are topological dynamical systems whose elements are sequences over a given finite alphabet. A translation-invariant measure on a subshift corresponds to a finite-valued stationary stochastic process. Measures obtaining maximal entropy are in some sense "most random" or "most uniform" among those with a given support. In this talk, I will present older and newer results of various authors regarding measures of maximal entropy.

Note for Attendees

Tea & cookies afterwards!
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Rachel Kuske and Alejandro Adem
UBC
Fri 25 Feb 2011, 3:00pm
Department Colloquium
MATX 1100
Presentation, call for submissions, and info session: NSERC Long-range Planning Exercise for Mathematics and Statistics
MATX 1100
Fri 25 Feb 2011, 3:00pm-4:00pm

Abstract

Background:
The Canadian mathematics and statistics communities are engaged in a long range planning (LRP) exercise for 2012-2017/22. This exercise is funded by NSERC, and draws on the expertise of the societies, institutes and the communities of researchers in mathematics and statistics. The site longrangeplan.ca serves as the primary repository for information about the development of the plan.

Members of the steering committee are visiting universities to as part of their community consultations.

In this capacity, Rachel Kuske and Alejandro Adem will give a short presentation on the process, and the progress to date, which will be followed by general discussion.

A call for submission of written documents has also been issued, and we welcome input from interested parties.  More details and guidelines for submission are provided on the home page of the website
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Sat 26 Feb 2011, 8:00am SPECIAL
One Time Event
UBC
Frontiers in Biophysics 2011 Conference
UBC
Sat 26 Feb 2011, 8:00am-6:00pm

Details

 
The call for abstracts for Frontiers in Biophysics 2011 is now open!  Please send your name, talk title, abstract, and affiliation (UBC, SFU, etc) to frontiersinbiophysics2011@gmail.com.  This is a one-day conference highlighting interdisciplinary research within the areas of biophysics and computational and mathematical biology in the greater Vancouver area.  Participants from undergraduates to emeritus are welcome and encouraged to attend and/or present a talk or poster.  The fifth annual conference of its kind, Frontiers in Biophysics 2011 will be held on the UBC campus in Vancouver on Saturday February 26, 2011. The schedule will include student presentations, a poster session, and a keynote address by Professor Tim Elston from the University of North Carolina.  

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George Bluman
UBC
Mon 28 Feb 2011, 3:00pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Nonlocally related systems III
Math Annex 1118
Mon 28 Feb 2011, 3:00pm-4:00pm

Abstract

We will continue with a historical development of the construction and uses of nonlocally related systems as well as open problems.
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UBC
Mon 28 Feb 2011, 3:00pm
Algebraic Geometry Seminar
WMAX 110
A multi-dimensional resolution of singularities with applications to analysis
WMAX 110
Mon 28 Feb 2011, 3:00pm-5:00pm

Abstract

The structure of the zero set of a multivariate polynomial is a topic of 
wide interest, in view of its ubiquity in problems of analysis, algebra, 
partial differential equations, probability and geometry. The study of 
such sets originated in the pioneering work of Jung, Abhyankar and 
Hironaka and has seen substantial recent advances in an algebraic setting.

In this talk, I will mention a few situations in analysis where the study of 
polynomial zero sets plays a critical role, and discuss prior work in this 
analytical framework in two dimensions. Our main result (joint with 
Tristan Collins and Allan Greenleaf) is a formulation of an algorithm for 
resolving singularities of a real-analytic function in any dimension with 
a view to applying it to a class of problems in harmonic analysis.
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UBC
Mon 28 Feb 2011, 4:30pm
Topology and related seminars
WMAX 110
Working seminar in Topology
WMAX 110
Mon 28 Feb 2011, 4:30pm-5:30pm

Abstract

This talk is a continuation on cyclic homology and Hochschild homology.
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