Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, August 29, 2013.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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1  2  3  4  5  6                1  2  3    1  2  3  4  5  6  7
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Thursday, August 29, 2013

11:00 am in 241 Altgeld Hall,Thursday, August 29, 2013

#### The range of Carmichael's universal exponent function

###### Kevin Ford (UIUC Math)

Abstract: Let $\lambda(n)$ denote the maximal order of an element of the group $(\mathbb{Z}/n\mathbb{Z})^*$, commonly called Carmichael's function. We will survey some results about the distribution of values of $\lambda(n)$ and present new, sharp estimates for the counting function of distinct values taken by $\lambda$ (joint with F. Luca and C. Pomerance).

12:30 pm in 464 Loomis Laboratory of Physics,Thursday, August 29, 2013

#### Organizational Meeting

Abstract: We will discuss possible topics and themes for the semester of common interest to the participating mathematicians and physicists. Please come prepared to suggest topics and/or speakers, or volunteer to give a talk yourself. This semester we will break from tradition and there will be periodic talks in Altgeld Hall.

1:00 pm in Altgeld Hall 347,Thursday, August 29, 2013

#### Organizational meeting

2:00 pm in 149 Henry Administration Building,Thursday, August 29, 2013

#### Tools for proving theorems using modular forms

###### Nick Andersen (UIUC Math)

Abstract: The graduate student number theory seminar is focused on "tools and methods used in number theory." In this informal student-run seminar, we will discuss the main tools that are used over and over again by those doing research in number theory. In my talk I will give a brief introduction to modular forms and discuss some important tools that are often used when one uses the theory of modular forms to prove things. I will conclude with a few brief examples, and I might even mention Ramanujan once or twice.

4:00 pm in 245 Altgeld Hall,Thursday, August 29, 2013

#### Complex and Arithmetic Dynamics in Dimension 1

###### Laura DeMarco (University of Illinois at Chicago)

Abstract: Questions about complex dynamical systems have traditionally been approached with techniques from analysis (complex or geometric). In the last 5 years or so, methods from arithmetic and algebraic geometry have played a central role -- and the result is an active new research area, the "arithmetic of dynamical systems" (to borrow the title of Silverman's textbook on the subject). The questions themselves have evolved, inspired by results from arithmetic geometry. In this talk, I will present joint work with Matt Baker, where we study "special points" within the moduli space of complex polynomial dynamical systems.