Department of

# Mathematics

Seminar Calendar
for Graduate Student Homotopy Theory Seminar events the year of Tuesday, February 23, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2021          February 2021            March 2021
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6       1  2  3  4  5  6
3  4  5  6  7  8  9    7  8  9 10 11 12 13    7  8  9 10 11 12 13
10 11 12 13 14 15 16   14 15 16 17 18 19 20   14 15 16 17 18 19 20
17 18 19 20 21 22 23   21 22 23 24 25 26 27   21 22 23 24 25 26 27
24 25 26 27 28 29 30   28                     28 29 30 31
31


Monday, January 25, 2021

3:00 pm in Zoom,Monday, January 25, 2021

#### Organisational meeting

###### Sai (UIUC)

Abstract: This is the organisational meeting for the graduate student homotopy theory seminar. Please email vb8 at illinois dot edu for the zoom details.

Monday, February 1, 2021

3:00 pm in Zoom,Monday, February 1, 2021

#### Thom spectra via rigid spaces

###### Heyi Zhu (UIUC)

Abstract: The classical definition of the space $GL_1(R)$ of units, given a ring spectrum $R$, does not play well with more modern models of spectra. In this talk, we will introduce Ando-Blumberg-Gepner-Hopkins-Rezk's Thom spectra functor, which builds upon a construction of $GL_1(R)$ as an $A_{\infty}$-space. If time permits, we will also briefly look at their $E_{\infty}$-version. Please email vb8 at illinois dot edu for the zoom details.

Monday, February 8, 2021

3:00 pm in Zoom,Monday, February 8, 2021

#### Spectral sequences and deformations of homotopy theories I

###### William Balderrama (UIUC)

Abstract: One of the oldest problems in stable homotopy theory is simple: just compute the stable homotopy groups of spheres. This turns out to be difficult, and a complete answer may never be known, but the computations continue. A recent technique being applied to great success can be summarized as: don't just compute the stable homotopy groups of the sphere spectrum, also compute the stable homotopy groups of other sphere spectra. These other sphere spectra include, for example, those arising in motivic and equivariant contexts, and can be thought of as deformations of the classical sphere spectrum. The homotopy theories they live in can then be thought of as deformations of classical stable homotopy theory. There are a few methods for building these deformations; the goal of this sequence of two talks is to describe the concrete approach to this deformation story using filtered objects. Please email vb8 at illinois dot edu for the zoom details.

Monday, February 15, 2021

3:00 pm in Zoom,Monday, February 15, 2021

#### Spectral sequences and deformations of homotopy theories II

###### William Balderrama (UIUC)

Abstract: One of the oldest problems in stable homotopy theory is simple: just compute the stable homotopy groups of spheres. This turns out to be difficult, and a complete answer may never be known, but the computations continue. A recent technique being applied to great success can be summarized as: don't just compute the stable homotopy groups of the sphere spectrum, also compute the stable homotopy groups of other sphere spectra. These other sphere spectra include, for example, those arising in motivic and equivariant contexts, and can be thought of as deformations of the classical sphere spectrum. The homotopy theories they live in can then be thought of as deformations of classical stable homotopy theory. There are a few methods for building these deformations; the goal of this sequence of two talks is to describe the concrete approach to this deformation story using filtered objects. Please email vb8 at illinois dot edu for the zoom details.

Monday, February 22, 2021

3:00 pm in Zoom,Monday, February 22, 2021

#### Structure of the Motivic Stable Homotopy Category

###### Brian Shin (UIUC)

Abstract: In classical homotopy theory, a first step in understanding the stable homotopy category is understanding the zeroth stable stem $\pi_0 \mathbf{S}$. The fact that this is the ring of integers leads to the idea that we may be able to study things "one prime at a time". In this expository talk, I'll talk about the analogous story in the setting of motivic homotopy theory. After reviewing basics of the motivic story, we'll see how knowledge of the motivic zeroth stable stem can be used to better understand the motivic stable homotopy category. Please email vb8 at illinois dot edu for the zoom details.