Seminar Calendar
for events the day of Friday, February 3, 2017.

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1  2  3  4  5  6  7             1  2  3  4             1  2  3  4
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Friday, February 3, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, February 3, 2017
 Del Edit Copy
Submitted by jjwen2.
 Eliana Duarte (UIUC Math)Syzygies and Implicitization of tensor product surfacesAbstract: A tensor product surface is the closure of the image of a map $\lambda:\mathbb{P}^1\times \mathbb{P}^1\to \mathbb{P}^3$. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of $\lambda$ in $\mathbb{P}^{3}$. Currently, syzygies and Rees algebras provide the fastest and most versatile method to find implicit equations of parameterized surfaces. Knowing the structure of the syzygies of the polynomials that define the map $\lambda$ allows us to formulate faster algorithms for implicitization of these surfaces and also to understand their singularities. We show that for tensor product surfaces without basepoints, the existence of a linear syzygy imposes strong conditions on the structure of the syzygies that determine the implicit equation. For tensor product surfaces with basepoints we show that the syzygies that determine the implicit equation of $\lambda$ are closely related to the geometry of the set of points at which $\lambda$ is undefined.

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 3, 2017
 Del Edit Copy
Submitted by anush.
 Anush Tserunyan (UIUC Math)On "Structurable equivalence relations" by R. Chen and A. Kechris: Universal equivalence relations (2nd talk)Abstract: In our previous talk, we stated the first main result of the paper: a characterization of the elementary classes of countable equivalence relations. In this second talk, we prove that every elementary class admits a $\sqsubseteq_B^i$-universal equivalence relation. This implies one direction of the aforementioned characterization.