Department of

Mathematics


Seminar Calendar
for Graduate Student Homotopy Theory Seminar events the year of Wednesday, September 11, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2019           September 2019          October 2019    
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Monday, January 14, 2019

3:00 pm in 343 Altgeld Hall,Monday, January 14, 2019

Organizational Meeting

Brian Shin (UIUC Math)

Monday, April 1, 2019

3:00 pm in 343 Altgeld Hall,Monday, April 1, 2019

Operadic Monoidal Structures

Tsutomu Okano (UIUC Math)

Abstract: In this talk I will discuss how (higher) operads help us encode monoidal structures in (higher) categories. I will also discuss how to generalize this to parametrized settings and hope to convey the usefulness of such formalism in equivariant and motivic homotopy theories.

Monday, April 8, 2019

3:00 pm in 343 Altgeld Hall,Monday, April 8, 2019

Mapping space spectral sequences

William Balderrama (UIUC Math)

Abstract: The classical story of obstruction theory for computing maps into a space Y involves lifting maps up the Postnikov tower of Y. In this talk, I will introduce a form of this obstruction theory for computing maps between highly structured objects in homotopy theory. Along the way, we will see why Quillen cohomologies show up in homotopy theory, take derived categories of derived categories, and take multiplicative Postnikov towers of nonconnective ring spectra.

Monday, April 15, 2019

3:00 pm in 343 Altgeld Hall,Monday, April 15, 2019

Group Theory for Homotopy Theorists

Brian Shin (UIUC Math)

Abstract: In this expository talk, we'll introduce a model structure on the category of groups and demonstrate how to effectively study groups using this model. This model has the technical advantage of avoiding the overly abstract definition of a group via sets with binary operation. It also allows for clean definitions of colimits and free objects. If time permits, we'll discuss monoidal structures for a certain localization of this model structure. This is based on a short article by Krause-Nikolaus.

Monday, April 22, 2019

3:00 pm in 343 Altgeld Hall,Monday, April 22, 2019

Complex structures on Real vector bundles

Abhra Abir Kundu (UIUC Math)

Abstract: In this talk, I will state the first and the second obstruction to having a stable complex structure on a real vector bundle. I will then show how one can go from stable complex structure to complex structure. And, if time permits, I will try to sketch how the second obstruction can be expressed as a secondary cohomology operation.

Monday, April 29, 2019

3:00 pm in 343 Altgeld Hall,Monday, April 29, 2019

Crystalline period map

Venkata Sai Bavisetty (UIUC Math)

Abstract: In Chromatic homotopy theory, one tries to understand the homotopy groups of spheres using the height filtration on formal group laws. This way at each height we get a spectral sequence whose $E_2$ term is the group cohomology of the Morava stabilizer group with coefficients in the Lubin-Tate ring. In this talk, I hope to explain a conceptual way to figure out the action of the Morava Stabilizer group on the Lubin-Tate ring.

Monday, August 26, 2019

3:00 pm in 441 Altgeld Hall,Monday, August 26, 2019

Organizational Meeting

Brian Shin (UIUC Math)

Monday, September 9, 2019

3:00 pm in 441 Altgeld Hall,Monday, September 9, 2019

Algebraic theories and homotopy theory

William Balderrama (UIUC Math)

Abstract: In this talk, I will motivate and introduce algebraic theories as a category-theoretic approach to finite product theories. I will then talk about a well-behaved notion of an infinitary algebraic theory, and the introduction of homotopy-theoretic structure, which can be used to define notions of homology and cohomology for the models of an algebraic theory. This is the first of two talks; the second will use these ideas to produce applications in stable homotopy theory.

Monday, September 16, 2019

3:00 pm in 441 Altgeld Hall,Monday, September 16, 2019

Modeling higher algebra with product-and-loop theories

William Balderrama (UIUC Math)

Abstract: In this talk, I will introduce the extra homotopical properties of a (suitably infinitary) algebraic theory that make it suitable for modeling spectral, or otherwise higher, algebra, rather than merely derived forms of ordinary algebra. To illustrate the utility of this viewpoint, I will indicate some of the computational tools that can be constructed and understood from this perspective. Time permitting, I will discuss some applications to chromatic homotopy theory.