Separating Square Principles at a Singular Cardinal

Speaker: 

Ryan Holben

Institution: 

UCI

Time: 

Monday, June 3, 2013 - 4:00pm to 5:30pm

Host: 

Martin Zeman

Location: 

RH 440R

Starting with a cardinal which is both subcompact and measurable, we produce a model in which \square_{\kappa,2} holds but \square_\kappa fails at a singular cardinal \kappa.  We will discuss several of the essential tools used, and also several ways in which this result may be extended.
 

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)).

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