Victor Ginsburg
I am a secondyear math Ph.D. student at UC Berkeley advised by Shirshendu Ganguly and Svetlana Jitomirskaya. Previously I was an undergraduate at Penn State.
I am supported by an NSF Graduate Research Fellowship.
My CV is here (updated December 18, 2023).
Email: [firstname] [at] math [dot] berkeley [dot] edu
Office: Evans Hall, Room 941
ORCID: https://orcid.org/0000000193996748
Research

Pinning, diffusive fluctuations, and Gaussian limits for halfspace directed polymer models.
Preprint.
arXiv:2312.11439.
Abstract:
Halfspace directed polymers in random environments are models of interface growth in the presence of an attractive hard wall. They arise naturally in the study of wetting and entropic repulsion phenomena. In 1985, Kardar predicted a "depinning" phase transition as the attractive force of the wall is weakened. This phase transition has been rigorously established for integrable models of halfspace last passage percolation (LPP), i.e. halfspace directed polymers at zero temperature, in a line of study tracing back to work of Baik–Rains. On the other hand, for integrable positive temperature models, the first rigorous proof of this phase transition has only been obtained very recently through a series of works of Barraquand–Wang, Imamura–Mucciconi–Sasamoto [IMS], Barraquand–Corwin–Das, and Das–Zhu [DZ] on the halfspace logGamma polymer. In this paper we study a broad class of halfspace directed polymer models with minimal assumptions on the random environment. We prove that an attractive force on the wall strong enough to macroscopically increase the free energy induces phenomena characteristic of the subcritical "bound phase," namely the pinning of the polymer to the wall and the diffusive fluctuations and limiting Gaussianity of the free energy. Our arguments are geometric in nature and allow us to analyze the positive temperature and zero temperature models simultaneously. Moreover, given the macroscopic free energy increase proven in [IMS] for the halfspace logGamma polymer, our arguments can be used to reprove the results of [IMS, DZ] on polymer geometry and free energy fluctuations in the bound phase.

On maps preserving Lie products equal to a rankone nilpotent.
With Hayden Julius and Ricardo Velasquez. (2020).
doi:10.1016/j.laa.2020.02.007
.
Abstract:
Let \(\phi\) be a bijective linear map on the algebra of
\(n\times n\) complex matrices such that \(\phi(e_{12})=e_{12}\) and \([\phi(A),\phi(B)]=e_{12}\) whenever \([A,B]=e_{12}\). The purpose of this paper is to describe \(\phi\). Surprisingly, \(\phi\) has a different description from maps preserving zero Lie products.
Teaching
I have served as a GSI (teaching assistant) for the following courses at UC Berkeley:
Spring 2023: Math 54 (Linear Algebra and Differential Equations) with John Lott.
Fall 2022: Math 54 (Linear Algebra and Differential Equations) with Vera Serganova.

