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 Events
Michele Klaus
Fri 8 Jul 2011, 9:00am SPECIAL
One Time Event
Graduate Student Center, Room 200
Doctoral Exam
Graduate Student Center, Room 200
Fri 8 Jul 2011, 9:00am-11:30am

Details

In the first part of the thesis we discuss the rank conjecture of Benson and Carlson. In particular, we prove that if G is a finite p-group of rank 3 and with p odd, or if G is a central extension of abelian p-groups, then there is a free finite G-CW-complex homotopy equivalent to the product of rk(G) spheres; where rk(G) is the rank of G.

We also treat an extension of the rank conjecture to groups of finite virtual cohomological dimension. In this context, for p a fixed odd prime, we show that there is an infinite group L satisfying the two following properties: every finite subgroup G<L is a p-group with rk(G)<3 and for every finite dimensional L-CW-complex homotopy equivalent to a sphere, there is at least one isotropy subgroup H<L with rk(H)=2.

In the second part of the thesis we discuss the study of homotopy G-spheres up to Borel equivalence. In particular, we provide a new approach to the construction of finite homotopy G-spheres up to Borel equivalence, and we apply it to give some new examples for some semi-direct products.


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Thomas Erneux
Universite Libre de Bruxelles, Belgium
Tue 12 Jul 2011, 2:00pm
Mathematical Biology Seminar
WMAX 110 (PIMS)
Applications of Delay Differential Equations
WMAX 110 (PIMS)
Tue 12 Jul 2011, 2:00pm-3:00pm

Abstract

I plan to review several applications described by delay differential equations (DDEs) starting from familiar examples such as car following models to physiology and industrial problems. DDEs have the reputation to be mathematically difficult but there is a renewed interest for both old and new problems. I’ll emphasize the need for analytical tools in order to guide our numerical simulations and identify key physical phenomena. These ideas will be illustrated by problems in nonlinear optics and neurobiology.

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UQAM
Mon 25 Jul 2011, 11:00am SPECIAL
Topology and related seminars
WMAX 110 (PIMS)
Left-orderability and Dehn surgery
WMAX 110 (PIMS)
Mon 25 Jul 2011, 11:00am-12:30pm

Abstract

There is a growing body of work that supports a connection between L-spaces and 3-manifolds with non-left-orderable fundamental group, in fact a Seifert fibred manifold is an L-space if and only if its fundamental group is not left-orderable. In this talk I'll provide evidence for a connection that extends beyond the class of Seifert fibred manifolds, by showing that L-spaces behave similarly to non-left-orderability with respect to the operation of Dehn surgery on a manifold. It is with this goal in mind one is led to define a decayed knot; decayed knots have the property that sufficiently large surgery always yields a manifold with non-left-orderable fundamental group. Moreover, cables of decayed knots are also decayed, as long as the ratio of the cabling coefficients is chosen to be large enough. I'll show how both of these properties mirror the behaviour of knots which admit L-space surgeries, and outline some questions for future research. This is joint work with Liam Watson.
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Miguel Raggi
Mon 25 Jul 2011, 12:30pm SPECIAL
One Time Event
Graduate Student Center, Room 200
Doctoral Exam
Graduate Student Center, Room 200
Mon 25 Jul 2011, 12:30pm-3:00pm

Details

We explore the field of Forbidden Configurations, a problem in
Extremal Set Theory. We consider a family of subsets of {1,2,...,m} as
the corresponding {0,1}-incidence matrix. For {0,1}-matrices F, A, we
say F is a *subconfiguration* of A if A has a submatrix which is a row
and column permutation of F. We say a {0,1}-matrix is *simple* if it
has no repeated columns. Let ||A|| denote the number of columns of A.
A {0,1}-matrix F with row and column order stripped is a
*configuration*. Given m and a family of configurations G, our main
function of study is forb(m,G) := max{||A|| : A simple and for all  F
in G, we have F not a subconfiguration of A }.

We give a general introduction to the main ideas and previous work
done in the topic. We develop a new more computational approach that
allows us to tackle larger problems. Then we present an array of new
results, many of which were solved in part thanks to the new
computational approach. We use both new ideas and new spins on old
ideas to tackle the problems. The new results include finding exact
bounds on small configurations that were previously unknown, and
proving some previously conjectured asymptotic bounds for "boundary''
configurations. We also develop a relationship between Forbidden
Configurations and Patterns, which we use to prove some results.
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Sungkyunkwan University, Korea
Mon 25 Jul 2011, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX110 (PIMS) --note the room change
On the blow-up problem for the Euler equations and the Liouville type results for the fluid equations
WMAX110 (PIMS) --note the room change
Mon 25 Jul 2011, 2:00pm-3:00pm

Abstract

In the first part of the talk we discuss some new observations on the blow-up problem in the 3D Euler equations. We consider the scenarios of  the self-similar blow-ups and the axisymmetric blow-up. For the self-similar blow-up we prove a Liouville type theorem for the self-similar Euler equations. For the axisymmetric case we show that some uniformity condition for the pressure is not consistent with the global regularity. In the second part we present Liouville type theorems for the steady Navier-Stokes equations for both of the incompressible and the compressible cases. In the time dependent case we prove that some pressure integrals have  definite sign unless the solution is trivial.

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The Chinese University of Hong Kong
Mon 25 Jul 2011, 3:00pm SPECIAL
Algebraic Geometry Seminar
MATH 126
SYZ mirror symmetry for toric manifolds
MATH 126
Mon 25 Jul 2011, 3:00pm-5:00pm

Abstract

In this talk, I will explain SYZ proposal on describing mirror symmetry as a Fourier-Mukia transformation along special Lagrangian torus fibration.  By computing certain open Gromov-Witten invariants, we show that the mirror map is the same as the SYZ map for certain toric Calabi-Yau manifolds.
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Iowa State University, Ames Iowa
Tue 26 Jul 2011, 12:00pm SPECIAL
Discrete Math Seminar
MATH 126
Recent results on the edit distance of graphs
MATH 126
Tue 26 Jul 2011, 12:00pm-1:00pm

Abstract

In this talk, we will discuss the edit distance function, a function of a hereditary property mathcal{H} and of p, which measures the maximum proportion of edges in a density-p graph that need to be inserted/deleted in order to transform it into a member of mathcal{H}. We will describe a method of computing this function and give some results that have been attained using it. The edit distance problem has applications in property testing and evolutionary biology and is closely related to well-studied Tur'an-type problems. The results we address will involve constructions used on the problem of Zarankiewicz as well as strongly regular graphs. This is joint work with Tracy McKay, Iowa State University.  
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Biao Li
Department of Mathematics, Ningbo University (China)
Wed 27 Jul 2011, 2:00pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Symmetry group direct methods and their applications
Math Annex 1118
Wed 27 Jul 2011, 2:00pm-3:00pm

Abstract

 In this talk, the symmetry group direct method and some applications for nonlinear systems are discussed. The direct method by Clarkson and Kruskal can derive symmetry reductions of a nonlinear system without using any group theory. Recently, the direct method has been modified to find the generalized Lie and non-Lie symmetry groups for some nonlinear systems. The Lie symmetry groups obtained via traditional Lie approaches are only special cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. Now, the direct method can be extended to construct some finite transformations between some variable-coefficient PDEs and their related  constant-coefficient PDEs or simpler variable-coefficient PDEs. These applications will be illustrated by some examples. 

This talk will be the first in a sequence of five talks on recent developments in Symmetries and Differential Equations.  All talks will take place from 2-3pm each Wednesday.  Future talks will take place in Math Annex 1102 and expected speakers include ZZ Yang, Ian Lisle, Jeremy Hoskins, Raouf Dridi and Shoufu Tian.
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