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 Events
UBC
Wed 1 Dec 2010, 3:00pm
Probability Seminar
MATH 126
The Unlikeliness of Being Covered
MATH 126
Wed 1 Dec 2010, 3:00pm-4:00pm

Abstract

We will show that the probability that a simple random walk will cover a finite, bounded degree graph in linear time is exponentially small.

More precisely, for every D and C, there exists a=a(D,C)>0 such that for any graph G, with n vertices and maximal degree D, the probability that a simple random walk, started anywhere in G, will visit every vertex of G in its first Cn steps is at most exp(-an).

Joint work with Itai Benjamini and Ben Morris.

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ENS
Wed 1 Dec 2010, 4:00pm
Probability Seminar
MATH 126
A view from infinity of the uniform infinite planar quadrangulation
MATH 126
Wed 1 Dec 2010, 4:00pm-5:00pm

Abstract

The Uniform Infinite Planar Quadrangulation (UIPQ) is an infinite planar graph which is the local limit of uniform planar quadrangulations of size n. It has been introduced by Krikun in 2005 following a pioneer work of Angel and Schramm on triangulations. The geometry of this object is particularly interesting, for example the volume growth exponent is 4. In this talk we introduce a new construction of the UIPQ and deduce several geometric properties. For example an essential uniqueness of infinite geodesics reminiscent of the work of Le Gall on the Brownian Map.

joint work in progress with L. Ménard and G. Miermont.

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Tasho Statev-Kaletha
Princeton University
Thu 2 Dec 2010, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Depth-zero local Langlands correspondence and endoscopic transfer
Room ASB 10900 (IRMACS - SFU Campus)
Thu 2 Dec 2010, 3:00pm-3:50pm

Abstract

The local Langlands correspondence seeks to parameterize the smooth irreducible representations of a reductive group G over a local field F in terms of Langlands parameters, objects closely related to representations of the Galois group of F. Each parameter is supposed to correspond to a finite set of representations of G, called an L-packet. The broad principle of Langlands functoriality suggests that often such an L-packet \Pi_G transfers to an L-packet \Pi_H on an endoscopic group H. The transfer is encoded in identities between the characters of representations in \Pi_G and those in \Pi_H. Endoscopic character identities play an important role not only in representation theory, but also in number theory, via the stabilization of the Arthur-Selberg trace formula.
 
In this talk, we will motivate the problem that the theory of endoscopy addresses, and then formulate the precise statement of the endoscopic character identities, after recalling the necessary notions from the local Langlands correspondence. If time permits, we will then discuss their proof for the depth-zero supercuspidal L-packets recently constructed by DeBacker-Reeder. The main technical tool involved is Waldspurger's work on endoscopy for p-adic Lie algebras, which ultimately rests on the fundamental lemma.

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 2 Dec 2010, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
On level lowering and level raising of modular forms
Room ASB 10900 (IRMACS - SFU Campus)
Thu 2 Dec 2010, 4:10pm-5:00pm

Abstract

Let f \in S_2(\Gamma_0(N)) be a modular newform of weight 2 and level N. Then given a prime ideal \lambda , in certain favourable cases, we can say if there is a modular newform g of weight 2 at level M such f \equiv g \pmod \lambda . When M|N this is a level lowering result, while when N |M this is a level raising result. In this talk I will discuss what happens when \lambda is not a prime ideal, but rather a power of a prime ideal.
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Athena Nguyen
UBC
Fri 3 Dec 2010, 12:30pm
Algebraic Groups and Related Structures
Math 126
(Algebraic Group -- Student Seminar) The quadratic form interpretation of Boch-Kato's conjecture
Math 126
Fri 3 Dec 2010, 12:30pm-1:30pm

Abstract

TBA
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McGill
Fri 3 Dec 2010, 1:30pm SPECIAL
PIMS Seminars and PDF Colloquiums
WMAX 110
Recent developments in the theory of complex multiplication
WMAX 110
Fri 3 Dec 2010, 1:30pm-2:30pm

Abstract

This is a seminar in the WENTS ("West End Number Theory Seminar") series.

Abstract:
In this talk we shall survey the theory of complex multiplication from its inception to the present and indicate some of the current outstanding challenges. The talk is in "colloquium style" and as such should be accessible to mathematicians that are not necessarily number theorists.
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UCSD
Fri 3 Dec 2010, 3:00pm
Department Colloquium
MATX 1100
(PIMS/UBC distinguished colloquium) The combinatorics of solving linear equations
MATX 1100
Fri 3 Dec 2010, 3:00pm-4:00pm

Abstract

 
A major branch of modern combinatorics, usually called Ramsey theory, studies properties of structures which are preserved under partitions. Its guiding philosophy can be neatly summarized by the statement, "Complete disorder is impossible". In this talk I will survey what is known and what is still unknown from this perspective for solution sets of linear equations over the integers. 

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UBC
Mon 6 Dec 2010, 1:30pm
Topology and related seminars
WMAX 110
Working seminar on homotopy theory of moduli spaces
WMAX 110
Mon 6 Dec 2010, 1:30pm-3:00pm

Abstract

This is the last talk of this series.

In the first half of the talk we will provide a global picture of how all the pieces (that we constructed throughout this series) fit together to prove Mumford's conjecture following the approach in Galatius, Madsen, Tillman and Weiss. In the second half we outline the proof of the last piece of information needed to complete the proof.

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