Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 27, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2014          October 2014          November 2014
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1  2  3  4  5  6             1  2  3  4                      1
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30


Monday, October 27, 2014

3:00 pm in 341 Altgeld Hall,Monday, October 27, 2014

#### Linear groupoid structures and representations up to homotopy

###### Rajan Mehta (Smith College)

Abstract: The notion of representation for a Lie groupoid has the annoying problem that it isn't generally possible to define a good adjoint representation. To fix this problem, Arias Abad and Crainic introduced the notion of "representation up to homotopy". In this talk, I will show how 2-term representations up to homotopy are related to linear groupoid structures, which play the role of semidirect products. There is a one-to-one correspondence at the level of isomorphism classes, but at the level of objects, the correspondence is noncanonical, so it is possible for certain constructions to be "natural" in one perspective but not the other. A key example that illustrates the value of linear groupoids is the adjoint representation. To define the adjoint representation up to homotopy of a Lie groupoid G, one needs to choose a distribution transverse to the source fibers. On the other hand, the linear groupoid that corresponds to the adjoint representation is canonical; it is simply the tangent bundle TG. This talk is based on joint work with Alfonso Gracia-Saz (arXiv:1007.3658).

4:00 pm in 243 Altgeld Hall,Monday, October 27, 2014

#### Topos Theory: Sketches of an Elephant

###### Nima Rasekh (UIUC Math)

Abstract: Although it's ideas and results are used in different branches of mathematics from set theory to differential and algebraic geometry, topos theory is still one of the more mysterious concepts of mathematics. In this talk I give a general introduction to the notion of a topos and some its applications. As it is the homotopy seminar, I will then move on to talk about topoi in the context of homotopy theory using the language of higher category theory. Finally, if time permits, I mention some unresolved issues regarding the connection between topoi and homotopy theory.

4:00 pm in 141 Altgeld Hall,Monday, October 27, 2014

###### Prof. Olcay Akman (Illinois State U.), Prof. Stephanie Alexander (U. of Illinois), Asst. Prof. Daniel Roberts (Illinois Wesleyan U.)

Abstract: All graduate students, postdocs and visiting faculty in Math are welcome at this informal panel discussion of academic careers at the different types of U.S. institutions. Bring your questions!

5:00 pm in Altgeld Hall,Monday, October 27, 2014

#### Introduction to free products

###### Alba Wafaa_Minyu Zhao (UIUC)

Abstract: We give an introduction to free products with amalgamation.

5:00 pm in 259 and 243 Altgeld Hall,Monday, October 27, 2014

Abstract: Graduating Math PhD students are invited to bring their academic job application materials (cover letter, CV, research statement, teaching statement etc.) and get on-the-spot feedback and advice from Prof. Olcay Akman (Illinois State U.), Asst. Prof. Daniel Roberts (Illinois Wesleyan U.), and Prof. Laugesen.