Apr 20

G&T Seminar
Bill Menasco (Buffalo)

Distance and intersection number in the curve complex

Abstract: Let $S_g$ be a closed oriented surface of genus $g \geq 2$ and $\mathcal{C}^1(S_g)$ be its curve complex—vertices are homotopy classes of essential simple closed curves with two vertices sharing an edge if they have disjoint representatives. It is known that $\mathcal{C}(S_g)$ is path connected , and the
distance, $d(\alpha , \beta)$, between two vertices $\alpha , \beta \in \mathcal{C}^1(S)$ is just the minimal count of the number of edges in an edge-path between $\alpha$ and $\beta$. One can also consider, $ i(\alpha , \beta)$, the minimal intersection between curve representatives of $\alpha$ and $\bet$. This talk discusses how $i(\alpha , \beta)$ will grow as $d(\alpha, \beta)$ grows. This is joint work with Dan Margalit.
4:00PM, Fri Apr 20 2018, 122 Math

Let $S_g$ be a closed oriented surface of genus $g \geq 2$ and $\mathcal{C}^1(S_g)$ be its curve complex—vertices are homotopy classes of essential simple closed curves with two vertices sharing an edge if they have disjoint representatives. It is known that $\mathcal{C}(S_g)$ is path connected , and the
distance, $d(\alpha , \beta)$, between two vertices $\alpha , \beta \in \mathcal{C}^1(S)$ is just the minimal count of the number of edges in an edge-path between $\alpha$ and $\beta$. One can also consider, $ i(\alpha , \beta)$, the minimal intersection between curve representatives of $\alpha$ and $\bet$. This talk discusses how $i(\alpha , \beta)$ will grow as $d(\alpha, \beta)$ grows. This is joint work with Dan Margalit.

Apr 23

Algebra Seminar- Joshua Eike from Brandeis University
Regular Languages and Growth in Groups
4:00PM, Mon Apr 23 2018, 250 Math Building

Given a generating set A for a group, we may write any group
element as a product of generators in A. Said another way, group elements
can be expressed as words in the alphabet A, and words in the generators
can be interpreted as elements of the group. This provides a connection
between group theory and formal language theory. Looking at minimal length
words expressing a group element allows us to define a metric on the group.
This gives us a connection to metric geometry. I will discuss a few of the
ways formal language theory, finite state automata, and geometry have been
used to study groups and how this motivated the work I am doing in
collaboration with Abdul Zalloum.

Apr 26

Tenured faculty meeting
4:00PM, Thu Apr 26 2018, 250 Math Bldg.

May 4

G&T Seminar
Angelica Deibel (Brandeis)
4:00PM, Fri May 4 2018, 122 Math

May 7

Algebra Seminar
Shizhuo Zhang, Indiana University
4:00PM, Mon May 7 2018, 250 Mathemtics Bldg.

May 11

Last Day of Classes
Friday, May 11, 2018