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 Events
Foster Tom
UBC
Thu 23 Oct 2014, 12:30pm
Graduate Student Seminar
Math 225
The probabilistic method
Math 225
Thu 23 Oct 2014, 12:30pm-1:45pm

Abstract

The probabilistic method, pioneered by Paul Erdős, is a means of proving the existence of a certain object. By describing a random process of choosing objects, if there is a nonzero probability of making a successful choice, then necessarily the desired kind of object exists. We present a problem in discrete math that employs this method.
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Avi Kulkarni
SFU
Thu 23 Oct 2014, 3:30pm
Number Theory Seminar
room ASB 10900 (SFU - IRMACS)
On Jacobians of dimension 2g that decompose into Jacobians of dimension g
room ASB 10900 (SFU - IRMACS)
Thu 23 Oct 2014, 3:30pm-4:30pm

Abstract

Let X be a genus 2g curve defined over an arbitrary field of characteristic not equal to 2 and let J(X) the Jacobian variety of X. We say that a Jacobian variety is decomposable if it is isogenous to a product of abelian varieties. The type of decomposition can by characterized by the type of kernel of the isogeny and the dimensions of the varieties in the product. We consider isogenies with kernel type (Z/2Z)g and products of dimension g Jacobian varieties. Additionally, we insist that the isogeny is polarized. In this talk we describe a family of (non-hyperelliptic) genus 2g curves whose Jacobians are decomposable in this way. We prove that all genus 4 curves whose Jacobian has this decomposition type are either in this family or arise from a different construction considered by Legendre. Joint work with Nils Bruin.
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Department of Mathematics, University of South Carolina
Fri 24 Oct 2014, 3:00pm
Department Colloquium
MATX 1100
A new asymptotic enumeration technique: the Lovasz Local Lemma
MATX 1100
Fri 24 Oct 2014, 3:00pm-4:00pm

Abstract

The lopsided version of the Lovasz Local Lemma gives asymptotically tight lower boundsfor a number of enumeration problems. In the configuration model matching upper bounds are available. In this way a number of asymptotic enumeration results, mostly due to Wormald and McKay, can be proved in an alternative way. A new result is asymptotic enumeration of graphs with respect to degree sequence and girth.  A classical probabilistic result of Paul Erdos showed the existence of graphs with arbitrary large girth and chromatic number. If the degree sequence satisfies some mild conditions, we show that almost all graphs with this degree sequence and prescribed girth have high chromatic number.
This is joint work with Lincoln Lu.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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PennState
Mon 27 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Rozansky--Witten-type invariants from symplectic Lie pairs
ESB 4127 (host: UBC)
Mon 27 Oct 2014, 3:00pm-4:00pm

Abstract

 In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be considered as an analogue of Chern-Simons type invariants, where the Atiyah class of the underlying complex manifold plays the role of  Lie bracket. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds. This is a joint work with Yannick Voglaire.
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Wes Maciejewski
UBC, Dept of Mathematics & CWSEI
Tue 28 Oct 2014, 12:30pm
Lunch Series on Teaching & Learning
MATH 126
Do we know how students view mathematics and how they study it?
MATH 126
Tue 28 Oct 2014, 12:30pm-1:30pm

Abstract

It has long been known that the way a student views the subject they study affects the approach they take to studying
the subject. This, in turn, affects their performance in the subject. It seems, then, that the improvement of student
outcomes not only requires addressing the approach a student takes to study, but also their view of the subject. In this presentation, I will present results from a series of surveys intended to explore two separate, but related questions:
1. Do math instructors actually know how their students view math?
2. What approaches to study do students take and how do these relate to their achievement?
The crucial aspect of this work is that the data gathered was analysed by course year. It turns out that the answers to both questions above are different for lower and upper-year courses.
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Mingfeng Zhao
Tue 28 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Traveling waves involving fractional Laplacians
ESB 2012
Tue 28 Oct 2014, 3:30pm-4:30pm

Abstract

In this talk, we will discuss the existence of the traveling wave solution for the Allen-Cahn equation involving the fractional Laplacians. Based on the existence of the standing waves for the balanced Allen-Cahn equation, we will use the continuity method to obtain the existence of the traveling waves for unbalanced Allen-Cahn equation. The key ingredient is the the bound of the traveling speed in terms of the potential. Some open questions will be discussed.
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University of Utah
Wed 29 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
Constructing aspherical manifolds with a given fundamental group
ESB 4133
Wed 29 Oct 2014, 3:15pm-4:15pm

Abstract

While an aspherical complex is determined up to homotopy by its fundamental group, there are many geometrically different aspherical manifolds with the same fundamental group. For instance, the punctured torus and the pair of pants look quite different, but both have the same fundamental group F_2. I will discuss constructions of aspherical manifolds for a given fundamental group, talk about the smallest dimension of such a manifold for a given group and describe some geometric invariants that distinguish different aspherical manifolds with the same fundamental group. I will discuss this for right angled Artin groups (joint work with Mike Davis, Boris Okun and Kevin Schreve) and possibly also for duality groups.
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