[Topology.beta] Fw: TopICS title and abstract

[Klang, I. (Inbar)]

Reminder that this is happening in Utrecht tomorrow.

—-
Inbar Klang
Assistant Professor, VU Amsterdam
Pronouns: she/her/hers
________________________________
From: TopICS-l <topics-l-bounces at lists.science.uu.nl> on behalf of Subramanian, V. (Vignesh) via TopICS-l <topics-l at lists.science.uu.nl>
Sent: Friday, November 14, 2025 3:59:02 PM
To: topics-l at lists.science.uu.nl <topics-l at lists.science.uu.nl>
Subject: [TopICS-l] TopICS title and abstract


Dear all,

Please find below the schedule and abstracts for the upcoming TopICS Seminar on Friday, 21st November 2025, in Utrecht.

Location and Time:
David de Wiedgebouw, Room DDW 0.42
13:30 to 17:30

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13:30 to 14:30
Marco Nervo (Utrecht Universiteit)
Title: A model for the Goodwillie tower of the circle

Abstract:
Computing the homotopy groups of spheres is a central problem in homotopy theory, and remains extremely difficult in the unstable setting. Goodwillie calculus offers a way to approximate spheres by spaces that agree with them on homotopy groups within a certain range. By making functorial a fiber sequence due to Gray, I will describe how each k-th approximation of a sphere can be expressed in terms of the (k–1)-st approximations together with the k-th approximation of the circle. To complete this inductive picture, I will present an explicit model for the k-th approximation of the circle, building on the work of Behrens and Kuhn on the Whitehead conjecture. I will also give examples of computations and discuss possible directions for further development.

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15:00 to 16:00
Connor Malin (MPIM Bonn)
Title: Some $k$-nilpotent algebras arising in the Goodwillie calculus of spaces

Abstract:
Given a pointed space $X$, Quillen demonstrated that the Lie algebra of primitive elements of the cocommutative Hopf algebra $C_\ast(\Omega X; \mathbb{Q})$ records the rational homotopy type of $X$. Using deformation theory of operads, we produce a cocommutative Hopf algebra for which the underlying algebra is $k$-nilpotent and describe when this allows us to recover the Goodwillie approximation $P_k(F)(X)$. By generalizing to iterated loop spaces, we are able to construct a $k$-nilpotent formal Lie algebra, in the sense of Shi, which encodes the same data. We conjecture that the grouplike elements and Maurer-Cartan elements, respectively, recover the so-called fake Goodwillie approximations $P_k^\mathrm{fake}(\mathrm{Id})(\Omega X),P_k^\mathrm{fake}(\mathrm{Id})(X)$.

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16:30 to 17:30
William Balderrama (University of Bonn)
Title: Unstable synthetic deformations

Abstract:
Homotopical structure can often be viewed as deforming algebraic structure. For example, the Postnikov tower of a connective ring spectrum R interpolates between the spectrum R and its 0th homotopy ring. Each map in this tower is a square-zero extension; this realizes R as a "nilpotent thickening" of π_0(R), and leads to a deformation theory for lifting algebraic things over π_0(R) to homotopical things over R.

I will talk about joint work with Piotr Pstrągowski that develops a nonabelian generalization of this, where connective ring spectra are replaced by certain higher algebraic theories. This provides further insight into Blanc-Dwyer-Goerss' style decompositions of moduli spaces in homotopy theory. Time permitting, I will sketch how this allows us to define categories of synthetic spaces, categorifying the unstable Adams spectral sequence.



You can also find this information in : https://sites.google.com/view/vigneshsubramanian/topics?authuser=0

Best regards,
Vignesh


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