Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 22, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, September 22, 2016

11:00 am in 241 Altgeld Hall,Thursday, September 22, 2016

#### Noncongruence modular form and Scholl representation

###### Tong Liu (Purdue University)

Abstract: In this talk, I will report the progress of the research on noncongruence modular form via the attached Galois representation (Scholl representation). As Scholl representations are motivic, they are expected to correspond to automorphic representations according to the Langlands philosophy. I will show this is the case for certain situations (potentially GL(2)-type) and explain how (potential) automorphy of Scholl representation relates to some standard conjectures of noncongruence modular form. This is joint work of Winnie Li and Ling Long.

1:00 pm in 347 Altgeld Hall,Thursday, September 22, 2016

#### Tiny Giants - Mathematics Looks at Zooplankton

###### Peter Hinow (Mathematics, University of Wisconsin, Milwaukee)

Abstract: Zooplankton is an immensely numerous and diverse group of organisms occupying every corner of the oceans, seas and freshwater bodies on the planet. They form a crucial link between autotrophic phytoplankton and higher trophic levels such as crustaceans, molluscs, sh, and marine mammals. Changing environmental conditions such as water temperatures, salinities and pH values currently create monumental challenges to their well-being. A signi cant subgroup of zooplankton are crustaceans of sizes between 1 and 10 mm. Despite their small size they have extremely acute senses that allow them to navigate their surroundings, escape predators, nd food and mate. In a series of joint works with Rudi Strickler (Department of Biological Sciences, University of Wisconsin - Milwaukee) we have investigated various behaviors of crustacean zooplankton. These include the visualization of the feeding current of the calanoid copepod Leptodiaptomus sicilis, the introduction of the \ecological temperature" as a descriptor of the swimming behavior of water eas Daphnia pulicaria and the communication by sex pheromones in copepods. The tools required for the studies stem from optics, ecology, neuroanatomy, computational uid dynamics, and computational neuroscience.

3:00 pm in 441 Altgeld Hall,Thursday, September 22, 2016

#### Intersection Homology and $L^2$ Cohomology

Abstract: Despite its name, singular homology is perhaps not the best topological tool for studying singular spaces. For a non-singular complex projective variety $X$, one has access to a host of classical results: Poincare duality, the de Rham theorem, the Hodge-Dolbeault isomorphism. For a singular variety many of these results no longer hold. One solution is intersection homology, which was developed by Goresky-MacPherson to modify singular homology in order to recover Poincare duality. In this talk we will (with lots of pictures!) motivate and introduce intersection homology and $L^2$ cohomology. Time permitting, we will discuss some open problems concerning what the de Rham theorem might look like for these new invariants.