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, 3:00pm4:00pm
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.
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PennState

Mon 27 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)

RozanskyWittentype invariants from symplectic Lie pairs

ESB 4127 (host: UBC)
Mon 27 Oct 2014, 3:00pm4:00pm
Abstract
In 1997, Rozansky and Witten built new finitetype invariants of 3manifolds 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 ChernSimons 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 RozanskyWittentype invariants of threemanifolds. This is a joint work with Yannick Voglaire.
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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, 12:30pm1:30pm
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 upperyear courses.
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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, 3:30pm4:30pm
Abstract
In this talk, we will discuss the existence of the traveling wave solution for the AllenCahn equation involving the fractional Laplacians. Based on the existence of the standing waves for the balanced AllenCahn equation, we will use the continuity method to obtain the existence of the traveling waves for unbalanced AllenCahn 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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Eindhoven University of Technology

Wed 29 Oct 2014, 3:00pm
Probability Seminar
ESB 2012

Degree distribution of shortest path trees and bias in network sampling algorithms

ESB 2012
Wed 29 Oct 2014, 3:00pm4:00pm
Abstract
In this talk, we investigate the degree distribution of shortest path trees of various weighted network models. The aim of many empirical studies is to determine the degree distribution of a network with unknown structure by using traceroute sampling. We derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights: the configuration model and rregular graphs with i.i.d. power law degrees and i.i.d. edge weights, the complete graph with edge weights that are powers of i.i.d. exponential random variables. We use these results to shed light on an empirically observed bias in network sampling methods.
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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, 3:15pm4:15pm
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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Emory University

Thu 30 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126

Hasse principles over function fields of padic curves

room MATH 126
Thu 30 Oct 2014, 3:30pm4:30pm
Abstract
Obstructions to the Hasse principle for the existence of rational points on principal homogeneous spaces under connected linear algebraic groups over a number field are well understood. Similar questions of Hasse principle have been studied over more general fields, particularly, function fields of curves over complete discrete valued fields. There are several positive results in this direction for connected linear algebraic groups which are rational, thanks to the patching techniques developed by HarbaterHartmannKrashen. We shall explain some recent progress and open questions concerning Hasse principle for function fields of padic curves.
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Note for Attendees
Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.