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Reminder that this is happening in Utrecht tomorrow.</div>
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—-</div>
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Inbar Klang</div>
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Assistant Professor, VU Amsterdam</div>
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Pronouns: she/her/hers</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> TopICS-l <topics-l-bounces@lists.science.uu.nl> on behalf of Subramanian, V. (Vignesh) via TopICS-l <topics-l@lists.science.uu.nl><br>
<b>Sent:</b> Friday, November 14, 2025 3:59:02 PM<br>
<b>To:</b> topics-l@lists.science.uu.nl <topics-l@lists.science.uu.nl><br>
<b>Subject:</b> [TopICS-l] TopICS title and abstract</font>
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<p class="x_MsoNormal" style="">Dear all,</p>
<p class="x_MsoNormal" style="">Please find below the schedule and abstracts for the upcoming TopICS Seminar on
<b>Friday, 21st November 2025</b>, in Utrecht.</p>
<p class="x_MsoNormal" style=""><b>Location and Time:</b><br>
David de Wiedgebouw, Room DDW 0.42<br>
13:30 to 17:30</p>
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<p class="x_MsoNormal" style=""><b>13:30 to 14:30</b><br>
<b>Marco Nervo (Utrecht Universiteit)</b><br>
<b>Title:</b> A model for the Goodwillie tower of the circle</p>
<p class="x_MsoNormal" style=""><b>Abstract:</b><br>
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.</p>
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<p class="x_MsoNormal" style=""><b>15:00 to 16:00</b><br>
<b>Connor Malin (MPIM Bonn)</b><br>
<b>Title:</b> Some $k$-nilpotent algebras arising in the Goodwillie calculus of spaces</p>
<p class="x_MsoNormal" style=""><b>Abstract:</b><br>
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 $P_k^\mathrm{fake}(\mathrm{Id})(\Omega X),P_k^\mathrm{fake}(\mathrm{Id})(X)$.</p>
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<p class="x_MsoNormal" style=""><b>16:30 to 17:30</b><br>
<b>William Balderrama (University of Bonn)</b><br>
<b>Title:</b> Unstable synthetic deformations</p>
<p class="x_MsoNormal" style=""><b>Abstract:</b><br>
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.</p>
<p class="x_MsoNormal" style="">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.</p>
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<p class="x_MsoNormal">You can also find this information in : <a href="https://sites.google.com/view/vigneshsubramanian/topics?authuser=0">
https://sites.google.com/view/vigneshsubramanian/topics?authuser=0</a></p>
<p class="x_MsoNormal" style="">Best regards,<br>
Vignesh </p>
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