Department of

Mathematics


Seminar Calendar
for events the day of Thursday, January 17, 2019.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2018           January 2019          February 2019    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                    1          1  2  3  4  5                   1  2
  2  3  4  5  6  7  8    6  7  8  9 10 11 12    3  4  5  6  7  8  9
  9 10 11 12 13 14 15   13 14 15 16 17 18 19   10 11 12 13 14 15 16
 16 17 18 19 20 21 22   20 21 22 23 24 25 26   17 18 19 20 21 22 23
 23 24 25 26 27 28 29   27 28 29 30 31         24 25 26 27 28      
 30 31                                                             

Thursday, January 17, 2019

11:00 am in 241 Altgeld Hall,Thursday, January 17, 2019

What is Carmichael's totient conjecture?

Kevin Ford (Illinois Math)

Abstract: A recent DriveTime commercial features a mathematician at a blackboard supposedly solving "Carmichael's totient conjecture". This is a real problem concerning Euler's $\phi$-function, and remains unsolved, despite the claim made in the ad. We will describe the history of the conjecture and what has been done to try to solve it.

12:00 pm in 243 Altgeld Hall,Thursday, January 17, 2019

Index properties of random automorphisms of free groups.

Ilya Kapovich (Hunter College)

Abstract: For automorphisms of the free group $F_r$, being "fully irreducible" is the main analog of the property of being a pseudo-Anosov element of the mapping class group. It has been known, because of general results about random walks on groups acting on Gromov-hyperbolic spaces, that a "random" (in the sense of being generated by a long random walk) element $\phi$ of $Out(F_r)$ is fully irreducible and atoroidal. But finer structural properties of such random fully irreducibles $\phi\in Out(F_r)$ have not been understood. We prove that for a "random" $\phi\in Out(F_r)$ (where $r\ge 3$), the attracting and repelling $\mathbb R$-trees of $\phi$ are trivalent, that is all of their branch points have valency three, and that these trees are non-geometric (and thus have index $<2r-2$). The talk is based on a joint paper with Joseph Maher, Samuel Taylor and Catherine Pfaff.