Department of

Mathematics


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

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, February 3, 2017

3:00 pm in 243 Altgeld Hall,Friday, February 3, 2017

Syzygies and Implicitization of tensor product surfaces

Eliana Duarte (UIUC Math)

Abstract: 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.

4:00 pm in 345 Altgeld Hall,Friday, February 3, 2017

On "Structurable equivalence relations" by R. Chen and A. Kechris: Universal equivalence relations (2nd talk)

Anush Tserunyan (UIUC Math)

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.

4:00 pm in 241 Altgeld Hall,Friday, February 3, 2017

Train Tracks on Surfaces

Marissa Loving (UIUC Math)

Abstract: Our mantra throughout the talk will be simple, "Train tracks approximate simple closed curves." Our goal will be to explore some examples of train tracks, draw some meaningful pictures, and develop an analogy between train tracks and another well known method of approximation. No great knowledge of anything is required for this talk as long as one is willing to squint their eyes at the blackboard a bit at times.