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 Events
Mark MacLean, Greg Martin, Steph van Willigenburg and Andrew Rechnitzer
Tue 1 Mar 2011, 3:00pm
One Time Event
MATH 126
Killam Winners Panel
MATH 126
Tue 1 Mar 2011, 3:00pm-4:00pm

Details

This event will feature a panel discussion involving four of the department's winners of the Killam Teaching Award. All are welcome to this event in the TA Accreditation Program Seminar Series. Refreshments will be served.
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Rice University
Tue 1 Mar 2011, 3:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (Note the time change to 3:00)
Bernstein's Theorem for the two-valued minimal surface equation.
WMAX 110 (Note the time change to 3:00)
Tue 1 Mar 2011, 3:00pm-4:00pm

Abstract

We explore the question of whether there are nontrivial solutions to the two-valued minimal surface (2MSE) equation defined over the punctured plane. The 2MSE is a non-uniformly elliptic PDE, degenerate at the origin, originally introduced by N.Wickramasekera and L.Simon to produce examples of stable branched minimal immersions.
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Tue 1 Mar 2011, 3:15pm
Stochastic Dynamics Working Group
IAM Lounge (LSK 306)
A Simple Escape Time Problem in Immunology
IAM Lounge (LSK 306)
Tue 1 Mar 2011, 3:15pm-4:15pm

Abstract


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University of Strasbourg/PIMS
Tue 1 Mar 2011, 3:30pm
Algebraic Groups and Related Structures
PIMS 216
Cohomological invariants from Rost's Chow groups
PIMS 216
Tue 1 Mar 2011, 3:30pm-4:30pm

Abstract

I will explain how to use Rost's theory of "Chow groups with coeffients" in order to effectively compute the cohomology invariants of (some) algebraic groups. The method is quite geometric and requires understanding the orbits of the group in at least one representation. One can also derive a useful spectral sequence from this approach.


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University of Tokyo
Tue 1 Mar 2011, 4:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (Note the time change to 4:00)
Fefferman's program in conformal geometry and the singularities of the Green functions of the conformal powers of the Laplacian
WMAX 110 (Note the time change to 4:00)
Tue 1 Mar 2011, 4:00pm-5:00pm

Abstract

Motivated by the analysis of the singularity of the Bergman kernel on strictly pseudoconvex complex domains, Fefferman launched in the late 70s the program of determining all local biholomorphic invariants of a strictly pseudoconvex complex domain. This program has since been extended to other "parabolic" geometries such as conformal geometry. After a review of Fefferman's program, we shall explain how to compute explicitly the logarithmic singularities of the Green kernels of the conformal powers of the Laplacian, including the Yamabe and Paneitz operators. As applications we obtain a new characterization of locally conformally flat manifolds and a spectral-theoretic characterization of the conformal class of the round sphere.
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UBC
Wed 2 Mar 2011, 4:00pm
Probability Seminar
MATH 126
Invariance Principle for the Random Conductance Model
MATH 126
Wed 2 Mar 2011, 4:00pm-5:00pm

Abstract

In this talk a quenched invariance principle for the random conductance model is presented.
More precisely, we consider a continuous time random walk X in an environment
of i.i.d. non-negative random conductances. In recent years  quenched invariance
principles have been proven for X under various assumptions on the law of the conductances,
while we present here the result for general i.i.d. environments.

This is joint work with Martin Barlow, Jean-Dominique Deuschel and Ben Hambly.
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Oleg Igoshin
Dept. of Bioengineering, Rice University
Thu 3 Mar 2011, 2:00pm
Mathematical Biology Seminar
WMAX 110
Uncovering self-organization mechanisms in Myxococcus xanthus swarms with modeling and image processing
WMAX 110
Thu 3 Mar 2011, 2:00pm-3:00pm

Abstract

Myxococcus xanthus is a model bacteria famous for its coordinated multicellular behavior resulting in formation of various dynamical patterns. Examples of these patterns include fruiting bodies - aggregates in which tens of thousands of bacteria self-organize to sporulate under starvation conditions and ripples - dynamical bacterial density waves propagating through the colony during predation. Relating these complex self-organization patterns in M. xanthus swarms to motility of individual cells is a complex-reverse engineering problem that cannot be solved solely by traditional experimental research. Our group addresses this problem with a complementary approach - a combination of biostatistical image quantification of the experimental data with agent-based modeling. To illustrate our approach we discuss our methods of modeling predatory traveling waves - ripples, quantifying emergent order in developmental aggregation under starvation conditions and discovering features that affect the aggregation dynamics.

Note for Attendees

This seminar will be held on a Thursday rather than our regular Tuesday.
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Alexander Molnar
SFU
Thu 3 Mar 2011, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Affine minimal rational functions
Room ASB 10900 (IRMACS - SFU Campus)
Thu 3 Mar 2011, 3:00pm-3:50pm

Abstract

Many arithmetic geometric results have an arithmetic dynamic analogue. For instance, Siegel's theorem that an elliptic curve has only finitely many integer points is analogous to the fact that any orbit under a rational function whose second iterate has non-constant denominator has only finitely many distinct integer values.
 
A conjecture of Lang states that the number of integer points on a minimal Weierstrass model of an elliptic curve is uniformly bounded. In order to translate this conjecture, one needs a dynamic concept of minimality. We present one such notion, affine minimality, an algorithm to compute affine minimal forms of rational functions and some recent results pertaining to the dynamical analogue of Lang's conjecture.

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 3 Mar 2011, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Friable values of polynomials
Room ASB 10900 (IRMACS - SFU Campus)
Thu 3 Mar 2011, 4:10pm-5:00pm

Abstract

We summarize the current meager state of knowledge concerning how often values of polynomials have only small prime factors (that is, the values are "friable" or "smooth"). We also present some evidence, in the form of a theorem conditional upon a suitably explicit hypothesis on prime values of polynomials, to support a conjectured asymptotic formula for the number of friable values of any polynomial.
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Queens
Fri 4 Mar 2011, 3:00pm
Department Colloquium
MATX 1100
Old and new perspectives on Hilbert functions
MATX 1100
Fri 4 Mar 2011, 3:00pm-4:00pm

Abstract

Hilbert functions are fundamental objects in algebraic geometry, commutative algebra, and combinatorics.  After recalling the basic definitions and motivating examples, we will discuss Macaulay's characterization for the collection of all Hilbert functions.  We'll then contrast this with a newer viewpoint and look at potential applications.
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Andrew Morrison
UBC
Mon 7 Mar 2011, 9:00am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) A geometric representation of the Heisenberg Algebra.
Math 126
Mon 7 Mar 2011, 9:00am-10:00am

Abstract

The Heisenberg algebra is defined by the relations;

[x_i,p_j] = \delta_{i,j} id.

Grojnowski and Nakajima constructed a geometric representation of this
algebra using correspondences between the collection of all the Hilbert
schemes of C^2.
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University of North Carolina
Mon 7 Mar 2011, 3:00pm
Algebraic Geometry Seminar
WMAX 110
A generalization of Fulton's conjecture for arbitrary groups
WMAX 110
Mon 7 Mar 2011, 3:00pm-5:00pm

Abstract

This is a report on my joint work with Prakash Belkale and Nicolas Ressayre.  We prove a generalization of Fulton’s conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.
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UBC
Mon 7 Mar 2011, 4:30pm
Topology and related seminars
WMAX 110
Working seminar in Topology
WMAX 110
Mon 7 Mar 2011, 4:30pm-5:30pm

Abstract

This is a working seminar in Topology. We will start a series of talk
about model categories
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UBC
Tue 8 Mar 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) A result of Tregub
Math 126
Tue 8 Mar 2011, 11:30am-1:00pm

Abstract

We start a series of talk on Amitsur's conjecture. In the first talk, we give some constructions of Brauer-Severi varieties. 
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Tue 8 Mar 2011, 3:15pm
Stochastic Dynamics Working Group
A Simple Escape Time Problem in Immunology (continued)
Tue 8 Mar 2011, 3:15pm-4:15pm

Abstract


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University of Washington and UBC
Tue 8 Mar 2011, 3:30pm
Algebraic Groups and Related Structures
PIMS 216
Divisors on Bott-Samelson varieties
PIMS 216
Tue 8 Mar 2011, 3:30pm-4:30am

Abstract

Given a sequence of roots, one can construct a corresponding Bott-Samelson variety.  These varieties are basic tools in representation theory and
geometry of G/P's; for instance,  the Bott-Samelson varieties corresponding to reduced sequences resolve singularities of Schubert varieties.  Partly because of these connections, a good understanding of line bundles and divisors, including descriptions of the nef and effective cones, is of interest.  In this talk, I'll explain what is known about these questions, what I would like to know, and how much I know of what I'd like to know.

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Connor Meehan
UBC
Tue 8 Mar 2011, 4:00pm
Discrete Math Seminar
Math 126
Forbidden Configurations and Repeated Induction
Math 126
Tue 8 Mar 2011, 4:00pm-5:00pm

Abstract

We discuss research conducted last summer by Dr. Anstee and the
speaker, with help from Miguel Raggi, in the extremal set theory
problem area of forbidden configurations. For an integer m and a given
(0,1)-matrix F, we define forb(m, F) (as you may remember!) as the
maximum number of columns that an m-rowed (0,1)-matrix A can have
subject to the conditions that A has no repeated columns and no
submatrix that is a row and column permutation of F. Let [G|H]
represent the concatenation of the matrices G and H, and let K(k)
denote the matrix of all possible (0,1)-columns on k rows. Fundamental
results determine forb(m, K(k)) and forb(m, [K(k)|K(k)]) exactly for
all m and k. Our research extends these results by identifying
matrices B, C such that forb(m, [K(k)|B]) = forb(m, K(k)) and forb(m,
[K(k)|K(k)|C]) = forb(m, [K(k)|K(k)]). Analysis of base cases tends to
be the most difficult part in applying standard induction techniques!
We also explain the motivation to consider a new function that is
somewhat opposite in spirit to forb (and appropriately named "req"!)
and its relation to the research problems.
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UBC
Wed 9 Mar 2011, 3:00pm
Undergraduate Colloquium
MATH 105
Turning your (infinitesimally thin) car around: Improving on the 3-point turn
MATH 105
Wed 9 Mar 2011, 3:00pm-4:00pm

Abstract

This week's UBC/UMC talk will be by Vince Chan.

Abstract: A set in the plane K is called a Kakeya set if a needle (i.e. a unit segment) can be continuously rotated around within K, returning to its original position with its ends reversed. In 1917, Soichi Kakeya asked for the minimal area for Kakeya sets, initially for convex sets but then expanded to include all sets. This talk will cover some of the ideas considered for this problem, including the "3-point turn", and a clever construction known as Besicovitch sets which answers a related problem. Kakeya and Besicovitch sets are useful in a surprising number of areas in mathematics; we will discuss their influence in one problem in harmonic analysis - convergence of partial Fourier integrals. No background is necessary for the discussion on construction of Kakeya sets, although knowledge of some Fourier analysis would help in the later portion of the talk.
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UBC
Wed 9 Mar 2011, 4:00pm
Probability Seminar
MATH 126
Branched polymers and Mayer expansions II
MATH 126
Wed 9 Mar 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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Joe Yuichiro Wakano
Meji Institute for Advanced Study of Mathematical Sciences
Thu 10 Mar 2011, 2:00pm
Mathematical Biology Seminar
WMAX 110
Mathematical expression of inclusive fitness theory
WMAX 110
Thu 10 Mar 2011, 2:00pm-3:00pm

Abstract


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Stanford
Fri 11 Mar 2011, 3:00pm
Department Colloquium
(Special PIMS Lecture: the inaugural Hugh C. Morris Lecture). CANCELLED
Uncertainty quantification and systemic
(Special PIMS Lecture: the inaugural Hugh C. Morris Lecture). CANCELLED
Fri 11 Mar 2011, 3:00pm-4:00pm

Abstract

The quantification of uncertainty in large-scale scientific and engineering computations is rapidly emerging as a research area that poses some very challenging fundamental problems which go well
beyond sensitivity analysis and associated small fluctuation theories. We want to understand complex systems that operate in regimes where small changes in parameters can lead to very different solutions. How are these regimes characterized? Can the small probabilities of large (possibly catastrophic) changes be calculated? These questions lead us into systemic risk analysis, that is, the calculation of probabilities that a large number of components in a complex, interconnected system will fail simultaneously.

I will give a brief overview of these problems and then discuss in some detail two model problems. One is a mean field model of interacting diffusions and the other a large deviation problem for conservation laws. The first is motivated by financial systems and the second by problems in combustion, but they are considerably simplified so as to carry out a mathematical analysis. The results do, however, give us insight into how to design numerical methods where detailed analysis is impossible.

Note for Attendees

Due to illness, PIMS regrets that the Friday, March 11 Hugh C. Morris Lecture with speaker George Papanicolaou has been cancelled. Our apologies for this late notice; we will reschedule this lecture for a later date.
 
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Athena Nguyen
UBC
Mon 14 Mar 2011, 10:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Spectral Sequence
Math 126
Mon 14 Mar 2011, 10:30am-12:00pm

Abstract

As the very first step of talking about spectral sequences in the context of étale cohomology, we review the basic theory of spectral sequence starting with spectral sequences associated to double complex. The goal with this series of talk is to describe the spectral sequence associated to Galois coverings.
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UBC
Mon 14 Mar 2011, 4:30pm
Topology and related seminars
WMAX 110
Working seminar in Topology
WMAX 110
Mon 14 Mar 2011, 4:30pm-5:30pm

Abstract

This is a continuation on the mini cycle about
Simplicial Presheaves in Topology and Algebraic Geometry
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UBC
Tue 15 Mar 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Universal Divison Algebras
Math 126
Tue 15 Mar 2011, 11:30am-1:00pm

Abstract

Using the theory of polynomial identity rings and the construction of the
universal division algebras, we will prove the following theorem:

Let k be a field, UD_n(k) the universal division ring of degree n over k,
and D a division ring of degree n whose centre contains k. If UD_n(k)
contains a (not necessarily maximal) subfield which is Galois over Z(UD_n)
with Galois group G, then D contains a subfield Galois over Z(D) with
Galois group G.

This was an important step in Amitsur's proof that the universal division
algebra is not a crossed product for certain values of n.
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Jennifer Trueblood
Cognitive Science Program, Indiana University, Bloomington
Tue 15 Mar 2011, 2:00pm
Mathematical Biology Seminar
WMAX 110
A Quantum Probability Model of Order Effects in Human Inference
WMAX 110
Tue 15 Mar 2011, 2:00pm-3:00pm

Abstract

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, new jury decision-making experiments are developed. The results of these experiments are used to compare the quantum model to the belief-adjustment model and suggest that the belief-adjustment model faces limitations whereas the quantum inference model does not.
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UBC
Tue 15 Mar 2011, 3:15pm
Stochastic Dynamics Working Group
IAM Lounge
A simple first passage problem that arises in an impacting system with noise
IAM Lounge
Tue 15 Mar 2011, 3:15pm-4:15pm

Abstract


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Kurt Luoto
UBC
Tue 15 Mar 2011, 4:00pm
Discrete Math Seminar
Math 126
Quasisymmetric and noncommutative Schur functions
Math 126
Tue 15 Mar 2011, 4:00pm-5:00pm

Abstract

Symmetric functions have applications in the real world as well as
many branches of mathematics.  The most important basis for the
algebra of symmetric functions is that of the Schur functions.  As
such they are much studied and have spawned many analogs and
generalizations. A combinatorial rule for the way they multiply is
given by the Littlewood-Richardson Rule.

In recent work, Haglund, Mason, van Willigenburg, and this author
introduced a family of quasisymmetric functions which we call
quasisymmetric Schur (QS) functions.  These naturally refine the
ordinary Schur functions and form a basis, over the integers, of QSym,
the quasisymmetric function algebra.

Dual to the QS functions are noncommutative analogs of the ordinary
Schur functions, having analogous properties such as a
Littlewood-Richardson rule and relationship to a poset of compositions
which is analogous to Young's lattice of partitions.  This is joint
work with Christine Bessenrodt and Stephanie van Willigenburg.

I will give a brief review of the combinatorics of ordinary Schur
functions in terms of tableaux.  Some familiarity with symmetric
functions is helpful, but is not necessary.  I will explain what
quasisymmetric functions are, then introduce you to these
quasisymmetric and noncommutative Schur analogs.

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UBC
Wed 16 Mar 2011, 4:00pm
Topology and related seminars
WMAX 110
Homotopy theory and spaces of representations
WMAX 110
Wed 16 Mar 2011, 4:00pm-5:00pm

Abstract

In this talk we will discuss properties of spaces of homomorphisms
Hom(Q,G) where Q is a discrete group and G a Lie group. The example
given by the ordered commuting n-tuples in a compact Lie group will be
explained in some detail. We will discuss how spaces of homomorphisms
and the descending central series of the free groups can be used to
construct a filtration of the classifying space BG. Homotopy properties
of these constructions will be given for finite groups, and cohomology
calculations provided for compact Lie groups. We will also describe
results on understanding both the number and stable homotopy type of
the components of related spaces of representations.
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ASU
Wed 16 Mar 2011, 4:00pm
Probability Seminar
MATH 126
Why is the frequency distribution of so much time series data near 1/f?
MATH 126
Wed 16 Mar 2011, 4:00pm-5:00pm

Abstract

A real-valued stationary time series is said to produce 1/f noise 
if the power spectral density is like 1/f on a long frequency interval. A 
question of interest since shot noise was noticed in the 1920's is the title 
of this talk. I will present some progress toward a general construction to 
explain such data and indicate some of the remaining questions.
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UBC
Thu 17 Mar 2011, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Fourier coefficients and Siegel theta series
Room WMAX 216 (PIMS - UBC Campus)
Thu 17 Mar 2011, 3:00pm-3:50pm

Abstract

Thanks to the work of Howe, Freitag, J.-S. Li, and most others, we can identify the holomorphic Siegel modular forms of degree n that arise as theta liftings associated with quadratic forms in at most n variables in terms of their Fourier coefficients. We shall review this work (using the language of theta correspondence) and discuss some ideas for studying the case when the number of variables in the quadratic form is greater than n.

Note for Attendees

Refreshments will be served between the two talks.
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Mike Hochman
Princeton University and Microsoft
Thu 17 Mar 2011, 3:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
On Zero temperature limits of Gibbs states
Math 126
Thu 17 Mar 2011, 3:30pm-5:00pm

Abstract


Let f be a Holder potential on the full one-sided shift {0,1}^N, N={0,1,2,...}, and let mu_beta denote the Gibbs measure for f at inverse temperature beta (existence and uniqueness are classical, as is the smooth dependence on beta). I will discuss the question of existence of the limit of these measures as beta tends to infinity, i.e. as the temperature tends to zero. Although over infinite state spaces it was known, due to work of Van Enter and Ruszel, that the limit may not exist, it was believed that over finite state spaces (e.g. the case {0,1} above) the measures should converge. In particular, for finite alphabets Bremont proved that convergence occurs when f takes only finitely many values. I will present joint work with Jean-Rene Chazottes in which we construct a counterexample, and discuss some of its features. If time permits I will also discuss results in the multidimensional case.

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UBC
Thu 17 Mar 2011, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Constructible exponential functions, integrability, and characters of p-adic groups
Room WMAX 216 (PIMS - UBC Campus)
Thu 17 Mar 2011, 4:10pm-5:00pm

Abstract

I will talk about a class of functions on local fields that can be defined by means of logic (the so-called constructible exponential functions). These functions are in a sense built from charactersitic functions of balls, and additive characters of the field. It turns out that they have unexpectedly simple "integration theory". It also turns out that Harish-Chandra characters of representations of p-adic groups near the identity element belong to this class of functions. This allows to transfer Harish-Chandra's theorem about local integrability of characters that was known in general only for local fields of characteristic zero, to large positive characteristic. All of the notions mentioned in this abstract will be defined in the talk.
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U. North Carolina at Chapel Hill
Fri 18 Mar 2011, 3:00pm
Department Colloquium
MATH ANNEX 1100 (PIMS/UBC distinguished colloquium)
Virtual Lung Project at UNC: What's Math Got to Do With It?
MATH ANNEX 1100 (PIMS/UBC distinguished colloquium)
Fri 18 Mar 2011, 3:00pm-4:00pm

Abstract

A group of scientists at the University of North Carolina, from theorists to clinicians, have coalesced over the past decade on an effort called the Virtual Lung Project.  There is a parallel VLP at the Pacific Northwest Laboratory, focused on environmental health, but I will focus on our effort.  We come from mathematics, chemistry, computer science, physics, lung biology, biophysics and medicine. The goal is to engineer lung health through combined experimental-theoretical-computational tools to measure, assess, and predict lung function and dysfunction.   Now one might ask, with all due respect to Tina Turner:  what's math got to do with it?  My lecture is devoted to many responses, including some progress yet more open problems.
 
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UBC
Mon 21 Mar 2011, 10:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Spectral Sequence
Math 126
Mon 21 Mar 2011, 10:30am-12:00pm

Abstract

We continue our survey about basic spectral sequences. In this talk we describe convergence of a first quadrant spectral sequence, and as examples the spectral sequence associated with a Serre fibration and a complete proof of the Wang sequence.
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UBC
Mon 21 Mar 2011, 3:00pm
Harmonic Analysis Seminar
MATH 126
On solution-free sets via local uniformity and energy incrementing
MATH 126
Mon 21 Mar 2011, 3:00pm-4:00pm

Abstract

We consider a system of k diagonal polynomials of degrees 1, 2,..., k.
Using methods developed by Gowers and refined by Green and Tao to obtain
bounds in the 4-term case of Szemeredi's Theorem on long arithmetic
progressions, we show that if a subset A of the natural numbers up to N of
size d_N*N exhibits sufficiently small local polynomial bias, then it
furnishes roughly the expected number of solutions to the given system.  If
A furnishes no non-trivial solutions to the system, then we show via an
energy incrementing argument that there is a concentration in a Bohr set of
pure degree k, and consequently in a long arithmetic progression.  We show
that this leads to a bound on the density d_N of the set A of the form d_N
<< exp(-c*sqrt(log log N)), where c>0 is a constant dependent at most on k.
 
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George Bluman
UBC
Mon 21 Mar 2011, 3:00pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Nonlocally related systems IV
Math Annex 1118
Mon 21 Mar 2011, 3:00pm-4:00pm

Abstract

We will continue with the historical development of systematic procedures to find nonlocally related but equivalent systems of PDEs and to use such systems to find nonlocal symmetries and nonlocal conservation laws of a given PDE system.  As a consequence, one is able to find and use symmetries for PDE systems which exhibit no Lie point symmetries and exhibit no local symmetries.
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University of Washington
Mon 21 Mar 2011, 3:00pm
Algebraic Geometry Seminar
WMAX 110
Irrational centers
WMAX 110
Mon 21 Mar 2011, 3:00pm-5:00pm

Abstract

Vanishing theorems and rational singularities are closely related and play important roles in classification theory as well as other areas of algebraic geometry. In this talk I will discuss these roles their interrelations and a new notion that helps understand these singularities and their connections to the singularities of the minimal model program and moduli theory of higher dimensional varieties.
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UBC
Mon 21 Mar 2011, 4:30pm
Topology and related seminars
WMAX 110
Working seminar in Topology
WMAX 110
Mon 21 Mar 2011, 4:30pm-5:30pm

Abstract

This is a continuation on the mini cycle about
Simplicial Presheaves in Topology and Algebraic Geometry
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UBC
Tue 22 Mar 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) A result of Tregub
Math 126
Tue 22 Mar 2011, 11:30am-1:00pm

Abstract

We start a series of talk on Amitsur's conjecture. In the first talk, we re-introduce Brauer-Severi varieties and discuss some constructions associated to projective representations of the group PGL_n. 
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Yue-Xian Li
Tue 22 Mar 2011, 3:15pm
Stochastic Dynamics Working Group
IAM Lounge
Noise-Induced Synchronization in Uncoupled Limit-Cycle Oscillators
IAM Lounge
Tue 22 Mar 2011, 3:15pm-4:15pm

Abstract


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Omer Angel
UBC
Tue 22 Mar 2011, 4:00pm
Discrete Math Seminar
Math 126
Random Graph Orderings
Math 126
Tue 22 Mar 2011, 4:00pm-5:00am

Abstract

We show that there is no interesting way to order the
vertices of a graph, and deduce a theorem about isometric embedding of
metric spaces in R^n.
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Domingos Marchetti
University of Săo Paulo
Wed 23 Mar 2011, 4:00pm
Probability Seminar
MATH 126
Hierarchical models: are they useful?
MATH 126
Wed 23 Mar 2011, 4:00pm-5:00pm

Abstract

The hierarchical spherical model is investigated at the critical point  
by solving the underlying evolution equation, corresponding to the  
renormalization group transformation in the limit as the block size  
goes to 1. Some limit theorems can be obtained following the  
trajectories of this PDE equation. Starting far away from the  
stationary Gaussian fixed point, an interpretation of the critical  
trajectory is given in terms of the geometric theory of functions  
which describes the motion of the Lee-Yang zeros under the scale  
transformation.

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UCL Louvain
Wed 23 Mar 2011, 4:00pm
Topology and related seminars
WMAX 110
On the homology of the space of long knots.
WMAX 110
Wed 23 Mar 2011, 4:00pm-5:00pm

Abstract

We consider the space L of long knots, i.e. of smooth embedding of the real line into a d-dimensional vector space R^d with a fixed behaviour at infinity. This space is almost the same as the space of all smooth embeddings of the circle into a d-dimensional sphere, Emb(S^1,S^d).
The fact that there is no knot in codimension > 2 implies that L is connected when d>3, but actually this space L is not contractible. In this talk I will explain how we can actually describe the homotopy type of that space. I will in particular explain that the rational homology of that space L is  computable as the homology of some explicit combinatorial chain complex of generalized chord diagrams. Another way of saying it is  that the  Vassiliev spectral sequence computing the rational homology  of L collapses at the E2-page. This fact is closely related to the fact that the
operad of little disks is formal.
Joint work with Victor Turchin and Ismar Volic
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Andrew Rechnitzer and Sandi Merchant
UBC
Thu 24 Mar 2011, 12:30pm
One Time Event
MATH 126
Lunch Series in Teaching and Learning (pizza lunch)
MATH 126
Thu 24 Mar 2011, 12:30pm-1:30pm

Details

Title: Building a diagnostic test for proof skills. Can we predict and increase success in an "introduction to proof" course?

One of our department's Carl Wieman Science Education Initiative projects is to assess and improve learning in our introductory proof course, Math 220.  As part of this project, we have been developing a short (<=20 min) test to administer at the start of the term to assess incoming students' basic logic, computational skills and mathematics reading comprehension. Such a diagnostic test could then be used to predict individual students' performance in the course and to inform us of gaps in student knowledge and skills.  In addition, by giving the test again at the end of term we can track learning gains and assess the effectiveness of any changes we are considering.

In this talk we will discuss our "first draft" and our first results from Math 220 students in Fall 2010. Already this uncovers some interesting results and we will discuss how the predictive power of the test compares with using results from Calculus II. We also hope to gain some feedback from department members on the test itself.  Are the skills we test the most important for learning mathematical proof?  Are there important skills missing?



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Felipe Garcia
UBC
Thu 24 Mar 2011, 3:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Raindrops in Vancouver seem to last forever
Math 126
Thu 24 Mar 2011, 3:30pm-5:00pm

Abstract

I will explain a method for constructing particle preserving cellular automata with no anticipation and velocity one, by showing that they must preserve a certain partial order. Some of this dynamical systems may be discrete models for the movement of drops of rain in a window, subject to a force that can be regarded as gravity or wind. I will also expose some related probability problems. E.g. What is the probability that a raindrop will continue to move forever (in an infinite window) subject to a sequence of wind directions (a random walk) ?
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Guillermo Mantilla-Soler
UBC
Mon 28 Mar 2011, 10:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Spectral Sequence
Math 126
Mon 28 Mar 2011, 10:30am-12:00pm

Abstract

We present the Lyndon–Hochschild–Serre spectral sequence in group cohomology and describe the associated 5-term short exact sequence associated to it.
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University of California, San Diego
Mon 28 Mar 2011, 3:00pm
Algebraic Geometry Seminar
WMAX 110
Generic strange duality for K3 surfaces
WMAX 110
Mon 28 Mar 2011, 3:00pm-4:00pm

Abstract

We consider moduli spaces of semistable sheaves on an elliptically fibered K3 surface, so that the first Chern class of the sheaves is a numerical section. For pairs of complementary such moduli spaces subject to numerical restrictions, we establish the strange duality isomorphism on sections of theta line bundles. We will also present applications to Brill-Noether theory for sheaves on a K3.
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George Bluman
UBC
Mon 28 Mar 2011, 3:00pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Nonlocally related systems V
Math Annex 1118
Mon 28 Mar 2011, 3:00pm-4:00pm

Abstract

We will continue with the historical development of systematic procedures to find nonlocally related but equivalent systems of PDEs and to use such systems to find nonlocal symmetries and nonlocal conservation laws of a given PDE system.  As a consequence, one is able to find and use symmetries for PDE systems which exhibit no Lie point symmetries and exhibit no local symmetries.
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UBC
Tue 29 Mar 2011, 11:30am
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) Amitsur's conjecture
Math 126
Tue 29 Mar 2011, 11:30am-1:00pm

Abstract

We present some examples of the method of reduction of structure in the wold of Brauer-Severi varieties.
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Somdatta Sinha
Centre for Cellular & Molecular Biology (CSIR), Hyderabad
Tue 29 Mar 2011, 2:00pm
Mathematical Biology Seminar
WMAX 110
Modelling infectious disease - from genomes to populations
WMAX 110
Tue 29 Mar 2011, 2:00pm-3:00pm

Abstract

Dr. Sinha's talk will cover both genome analysis of pathogens (HIV-1 in particular), SIR type models, and statistical modelling of disease prevalence data (of Malaria).
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Tue 29 Mar 2011, 3:15pm
Stochastic Dynamics Working Group
IAM Lounge
Noise-Induced Synchronization in Uncoupled Limit-Cycle Oscillators, Continued
IAM Lounge
Tue 29 Mar 2011, 3:15pm-4:15pm

Abstract


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Masoud Kamgarpour
UBC
Tue 29 Mar 2011, 3:30pm
Algebraic Groups and Related Structures
PIMS 216
Geometrization of principal series representations 
PIMS 216
Tue 29 Mar 2011, 3:30pm-4:30pm

Abstract

Let G be a connected reductive group over F_q((t)) and let B be a Borel subgroup. Principal series representations are realized on the space of twisted functions (equivalently, sections of line bundles) on G/B. To geometrize this, in the frame work of geometric Langlands program, we would like to replace functions by perverse sheaves. The trouble is that G/B is infinite dimensional (as a variety over F_q) and so it is not clear how to define perverse sheaves on such objects. I will explain how to overcome this difficulty by employing methods of Howe-Bushnell-Kutzko-Roche to realize (families of) principal series representations via compact subgroups. 


 

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Ed Richmond
UBC
Tue 29 Mar 2011, 4:00pm
Discrete Math Seminar
Math 126
The Honeycomb model and tight fusion frames
Math 126
Tue 29 Mar 2011, 4:00pm-5:00pm

Abstract

A tight fusion frame is a sequence of orthogonal projection matrices which
sum to a scalar multiple of the identity.  To any such sequence, we can
associate a weakly decreasing sequence of positive integers given by the
ranks of these projections.  The question we address is the following:

For which sequences of positive integers do tight fusion frames exist?

In this talk, I will discuss ongoing work with K. Luoto and M. Bownik where
we explore this problem.  One of our main tools is the Knuston-Tao
Honeycomb Model.  In particular, we use the Honeycomb model to prove
majorization of tight fusion frames.  Majorization gives a partial order
structure on sequences for which tight fusion frames exist.

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Mohammad Fallahi-Sichani
University of Michigan
Wed 30 Mar 2011, 1:00pm
Mathematical Biology Seminar
Math 126
Multi-scale analysis of TNF-regulated immune response to Mycobacterium tuberculosis infection
Math 126
Wed 30 Mar 2011, 1:00pm-2:00am

Abstract

Tuberculosis (TB) granulomas are organized collections of immune cells that form in the lung as a result of immune response to Mycobacterium tuberculosis (Mtb) infection. Formation and maintenance of granulomas are essential for control of Mtb infection and are regulated in part by a pro-inflammatory cytokine, tumor necrosis factor‐α (TNF). We have developed a multi-scale computational model that includes molecular, cellular and tissue scale events that occur during TB granuloma formation. At the molecular scale, we focus on TNF. TNF receptor internalization kinetics are predicted to play a critical role in infection outcome, controlling whether there is clearance of bacteria, excessive inflammation, containment of bacteria in a stable granuloma, or uncontrolled growth of bacteria. Our results suggest that there is an inter-play between TNF and bacterial levels in a granuloma that is controlled by the combined effects of both molecular and cellular scale processes. We also use the model to explain what mechanisms lead to differential effects of TNF-neutralizing drugs (generally used to treat anti-inflammatory diseases) on reactivation of TB. Ultimately, these results can help to elaborate relevant features of the immune response to Mtb infection, identifying new strategies for therapy and prevention.

Note for Attendees

Note the unusual place and time.
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Ravi Vakil, Stanford University
Wed 30 Mar 2011, 1:30pm SPECIAL
One Time Event
Geography 100
Niven Lecture
Geography 100
Wed 30 Mar 2011, 1:30pm-2:30pm

Details


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UBC
Wed 30 Mar 2011, 4:00pm
Probability Seminar
MATH 126
Branched polymers and Mayer expansions III
MATH 126
Wed 30 Mar 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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Guillaume Maurin
UBC
Thu 31 Mar 2011, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Polynomial equations with constant coefficients over function fields
Room ASB 10900 (IRMACS - SFU Campus)
Thu 31 Mar 2011, 3:00pm-3:50pm

Abstract

We will present new conjectures on polynomial equations with constant coefficients over a function field of arbitrary characteristic (joint work with Ghioca). These statements are inspired by previous conjectures from Zilber, Pink and Bombieri, Masser and Zannier. We will try to explain how known results on the latter may give some information on the former in the case of characteristic zero.

Note for Attendees

Refreshments will be served between the two talks.
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Nishant Chandgotia
UBC
Thu 31 Mar 2011, 3:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Hammersley-Clifford Theorem
Math 126
Thu 31 Mar 2011, 3:30pm-5:00pm

Abstract


Hammersley Clifford Theorem gives us the equivalence of Markov random fields and measures with a nearest neighbour Gibb's potential  on finite graphs provided that the measure is fully supported. This generalises naturally when the graph is infinite. However it fails to hold when the measure is not fully supported. We will discuss the theorem and some examples for which it fails. 
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UBC
Thu 31 Mar 2011, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
On additive combinatorics in higher degree systems
Room ASB 10900 (IRMACS - SFU Campus)
Thu 31 Mar 2011, 4:10pm-5:00pm

Abstract

We consider a system of k diagonal polynomials of degrees 1, 2,..., k. Using methods developed by W.T. Gowers and refined by Green and Tao to obtain bounds in the 4-term case of Szemeredi's Theorem on long arithmetic progressions, we show that if a subset A of the natural numbers up to N of size d_N*N exhibits sufficiently small local polynomial bias, then it furnishes roughly the expected number of solutions to the given system.  If A furnishes no non-trivial solutions to the system, then we show via an energy incrementing argument that there is a concentration in a Bohr set of pure degree k, and consequently in a long arithmetic progression.  We show that this leads to a bound on the density d_N of the set A of the form d_N << exp(-c*sqrt(log log N)), where c>0 is a constant dependent at most on k.
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