D. Shlyakhtenko

activity

20242026

collaborators

5 papers

math.OA2026

Failure of Strong Convergence of Matrices with Fermionic Entries

Dimitri Shlyakhtenko

Let $Q_{N}^{(k)}$ be an $N \times N$ matrices with entries satisfying CAR, normalized to have variance $1/ N$ with respect to the trace of the CAR algebra. We show that, althoug…

math.OA2026

A Free Analog of Bobkov's Gaussian Isoperimetry Inequality

Dimitri Shlyakhtenko

We prove a one-variable functional inequality which is the free probability analog of Bobkov's isoperimetry inequality. The inequality involves the $L^{1}$ norm of the difference quo…

math.OA2025

Establishing strong 1-boundedness via non-microstates free entropy techniques

Benjamin Major, Dimitri Shlyakhtenko

We show that, for many choices of finite tuples of generators $X = (x_{1}, \dots, x_{d})$ of a tracial von Neumann algebra $(M, I ¨ )$ satisfying certain decomposition properties (non-p…

math.AC2025

The reciprocal complement of a polynomial ring in several variables over a field

Neil Epstein, Lorenzo Guerrieri, K. Alan Loper

The *reciprocal complement* $R (D)$ of an integral domain $D$ is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R (D)$ ar…

math.NT2024

Rank growth of elliptic curves in $S_{4}$ and $A_{4}$ quartic extensions of the rationals

Daniel Keliher

We investigate the rank growth of elliptic curves from $Q$ to $S_{4}$ and $A_{4}$ quartic extensions $K / Q$ . In particular, we are interested in the quantity $\mathrm{…