This Week in Mathematics


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Entries for this week: 3

Tuesday February 03, 2026

Rognes’ connectivity conjecture
- Jeremy Miller, Purdue University
Time: 3:05PM Room: Zoom
Abstract/Desc: Rognes’ connectivity conjecture concerns the connectivity of a simplicial complex called the common basis complex. Rognes proved that the equivariant homology of this complex is the E^1 page of a spectral sequence converging to the homology of the algebraic K-theory spectra. I will describe joint work with Patzt and Wilson where we prove the connectivity conjecture for fields. I will explain a connection between the homology the common basis complex and the André–Quillen homology of a certain equivariant ring built out of Steinberg modules. Time permitting, I will mention variants of these results for symplectic groups (joint with Scalamadre and Sroka) and automorphism groups of free groups (joint with Bruck and Piterman).

Thursday February 05, 2026

Financial Math
VIX Options in the Short-Maturity Regime
- Lingjiong Zhu,
Time: 3.05 Room: LOV 231
Abstract/Desc: We derive the short-maturity asymptotics for VIX option prices in local-stochastic volatility models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the asymptotics for the OTM options are expressed as a two-dimensional variational problem, which is reduced to an extremal problem for a function of two real variables. This extremal problem is solved explicitly in an expansion in log-moneyness. We will study the VIX option pricing for Heston-type model and the SABR model in more detail. Finally, we will discuss VIX option pricing in the presence of jumps. This is based on the joint work with Desen Guo, Dan Pirjol and Xiaoyu Wang.

Algebra seminar
TBA
- Veronica Arena, Cambridge
Time: 3:05pm Room: Zoom
Abstract/Desc: TBA

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Department of Mathematics

This Week in Mathematics