# Graduate Colloquium Fall 2018

McHenry Library Room 4130

Refreshments served at 3:30 in room 4161

For further information, please contact Graduate Student John McHugh or call 831-459-2969

**Wednesday October 10th, 2018**

No Seminar

**Wednesday October 17th, 2018**

No Seminar

**Wednesday October 24th, 2018**

No Seminar

**Wednesday October 31st, 2018**

**Kim Stubbs, UCSC***Geometric Representations of Dedekind's Proof of Irrationality*

In $\textit{Essays on the Theory of Numbers}$, Richard Dedekind gives a general algebraic proof that if D is a positive integer that is not the square of an integer, then $\sqrt{D}$ is irrational. In the 1960's, Stanley Tennenbaum gives the geometric representation of Dedekind's proof for which $D = 2$. In this talk we'll look at the geometric representations of Dedekind's proof for which $D = 3, 5, 6, 8,12,15,24\, \text{and}\, 48$ and their constructions which are similar to the construction for the $D = 2$ case.

**Wednesday November 7th, 2018**

No Seminar

**Wednesday November 14th, 2018**

Seminar rescheduled to 12/05/18

**Wednesday November 21st, 2018**

No Seminar

**Wednesday November 28th, 2018**

**Victor Bermudez, UCSC**

**Wednesday December 5th, 2018**

**Zheng Zhou, UCSC**

*Asymptotics of Determinants for Finite Sections of Operators with Almost Periodic Diagonals*

Toeplitz operators are of importance in connection with problems in physics and probability theory. While the classical Strong Szeg\"{o}-Widom limit theorem has been settled over Toeplitz operators with smooth symbols or Fisher-Hartwig symbols, whose diagonals are periodic sequences, I am going to give a brief description of asymptotics of determinants of operators whose diagonals are almost periodic sequences instead. This generalizes the classical limit theorem for block Toeplitz operators, and gives rises to an inverse closedness problem.