Germán Stefanich

Bing postdoctoral fellow,
Department of Mathematics,
University of Texas at Austin.
PMA 10.170
gstefanich(at)utexas(dot)edu

I am a Bing postdoctoral fellow at the University of Texas at Austin. Previously, I was a student of David Nadler at the University of California at Berkeley. I am interested in higher category theory and derived algebraic and symplectic geometry. Here is my CV.

Research

• Tannaka duality and 1-affineness
Establishes an affineness result in the theory of sheaves of categories and applies it to Tannaka duality and to the study of relative tensor products and higher traces of ∞-categories of quasicoherent sheaves.
• Derived ∞-categories as exact completions
Develops the theory of exact completions of regular ∞-categories and shows that in the additive context it recovers the theory of connective derived ∞-categories.
• Classification of fully dualizable linear categories
Provides a description of the fully dualizable objects in the symmetric monoidal 2-category of cocomplete categories linear over a G-ring.
• Derived Mellin Transform (With Tom Gannon)
This is an appendix to "Classification of nondegenerate G-categories" by Tom Gannon. Establishes an ∞-categorical version of the Mellin transform for D-modules on a torus.
• Higher Quasicoherent Sheaves
My PhD thesis. The first half contains a number of results in the theory of enriched higher categories, culminating in a discussion of monads and the enriched monadicity theorem. The second half builds upon the two papers below and develops the theory of quasicoherent sheaves of (∞, n)-categories in derived algebraic geometry.
• Higher sheaf theory I: Correspondences
Studies the problem of constructing representations of a higher category of correspondences. This is the first part of a series of papers that develop the theory of sheaves of higher categories in derived algebraic geometry.
• Presentable (∞, n)-categories
Introduces a notion of presentable higher categories, and establishes some basic technical properties that will be used in the higher sheaf theory sequence.

Other writing

• Cohomological methods in differential equations
My undergraduate thesis. Studies the theory of obstructions to the formal integrability of partial differential equations and its application to the equivalence problem for G-structures.
• Talk notes
Notes from some graduate seminars.