An Odyssey into Dimensions

In the 1884 classic, "Flatland: A Romance of Many Dimensions," Edwin A. Abbott described a world where the inhabitants living in two dimensions are visited every millennium by an alien-like visitor from the world of three dimensions.  Although the book was written as a social satire, it does raise the interesting question whether there are extra dimensions that we are not currently aware of?  We shall analyse this question mathematically and see how the number and type of dimensions can have a big effect for statements in geometry.

Joux's Recent Index Calculus Results, Part II: The Function Field Sieve and Joux's Improvements.

Speaker: 

Joshua Hill

Institution: 

UCI

Time: 

Tuesday, June 4, 2013 - 3:00pm

Host: 

Alice Silverberg

Location: 

RH 340N

In this talk, I describe the Function Field Sieve algorithm and its
application to solving the discrete log problem, highlighting Joux's
recent advancements that reduce the heuristic work factor to L(1/4 + o(1)).

Changes of the filtration and the default event risk premium

Speaker: 

Delia Coculescu

Institution: 

Univsitat Zurich

Time: 

Wednesday, May 29, 2013 - 2:00pm to 3:00pm

Host: 

Michael C. Cranston

Location: 

RH 440R

In this talk we aim at emphasizing the role of information in financial markets (public information versus insider information). In particular, if the information about a particular event (as for instance the default event of a company) is incorporated into a pricing model, then by a change of the underlying filtration, one can compute risk premiums attached to particular events. We also show that modeling of the information leads eventually to modeling of dependencies.

Limit stochastical differential equations (SDEs) for products of random matrices in a critical scaling.

Speaker: 

Christian Sadel

Institution: 

U Vancouver

Time: 

Tuesday, May 28, 2013 - 2:00pm

Location: 

RH 340P

joint work with Balint Virag.

abstract:
We consider the Markov process given by products of i.i.d. random
matrices that are perturbations of a fixed non-random matrix and the
randomness is coupled with some small coupling constant.
Such random products occur in terms of transfer matrices for random
quasi-one dimensional Schroedinger operators with i.i.d. matrix potential.
Letting the number of factors going to infinity and the random disorder
going to zero in a critical scaling we obtain a a limit process for a
certain Schur complement of the random products. This limit is described
by an SDE. This allows us to obtain a limit SDE for the Markov processes
given by the action of the random products on Grassmann manifolds.

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