Department of

# Mathematics

Seminar Calendar
for events the day of Monday, February 9, 2015.

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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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Monday, February 9, 2015

12:00 pm in 341 AH,Monday, February 9, 2015

#### Symplectic non-squeezing in Hilbert space

###### Alex Tumanov (UIUC Math)

Abstract: The celebrated Gromov's non-squeezing theorem of 1985 says that the unit ball $B^{2n}$ in $R^{2n}$ can be symplectically embedded in the "cylinder" $rB^2 \times R^{2n-2}$ of radius $r$ only if $r\ge 1$. I present a generalization of this theorem for Hilbert space. The result can be applied to symplectic flows of Hamiltonian PDEs. This work is joint with Alexander Sukhov.

4:00 pm in 145 Altgeld Hall,Monday, February 9, 2015

#### The Quot scheme and representability of moduli problems

###### Matej Penciak   [email] (UIUC Math)

Abstract: This is the first of two talks in which I will describe the Quot scheme--a scheme that represents a general moduli problem of quotients of a fixed coherent sheaf. The generality of the Quot scheme makes it an important stepping stone in proving the representability of moduli problems arising in algebraic geometry. In this talk I will begin with a discussion of general moduli problems, the definition of the Quot scheme, and how it is related to common moduli spaces such as Hilbert schemes, and moduli of curves. I will end with a strategy by sketching the construction of the Quot scheme which will be explored in more detail in the second talk.

5:00 pm in 241 Altgeld Hall,Monday, February 9, 2015

#### Khintchine inequalities

###### Minyu Zaho and Li Gao (UIUC Math)

Abstract: We will finish the proof for Khintchine and Voiculescu's inequality and start with p<1