Currently, I am a Visiting Assistant Professor at the Department of Mathematics of the University of Arkansas https://math.uark.edu/directory/index/uid/souvikd/name/Souvik+Dey/
Before this, I was a Postdoctoral fellow in the Department of Algebra at Charles University, Prague. I received my PhD from University of Kansas, USA, under the supervision of Professor Hailong Dao, in Summer 2023.
Email: souvikd@uark.edu, dey0976@gmail.com
Prague email(which I still have access to for a few months): souvik.dey@matfyz.cuni.cz
My broad area of interest is in Algebra, mainly Commutative Algebra and its interactions with Algebraic Geometry, Combinatorics, Homological Algebra, Representation Theory and Algebraic K-theory. I also occasionally like to think about Number Theory, and Algebraic Topology.
Publications and Preprints
Exact subcategories, subfunctors of $\text{Ext}$, and some applications; joint with Hailong Dao and Monalisa Dutta; Nagoya Mathematical Journal, DOI: 10.1017/nmj.2023.29.
Vanishing of (co)homology of Burch and related submodules, joint with Toshinori Kobayashi; Illinois J. Math. 67(1): 101-151 (April 2023). DOI: 10.1215/00192082-10429128.
On the reducing projective dimension over local rings, joint with Olgur Celikbas, Toshinori Kobayashi, Hiroki Matsui, Glasgow Mathematical Journal , First View , pp. 1--15, DOI: 10.1017/S0017089523000368.
On the Subcategories of n-Torsionfree Modules and Related Modules, joint with Ryo Takahashi ; Collect. Math. 74, 113–132 (2023). https://doi.org/10.1007/s13348-021-00338-1.
Comparisons between Annihilators of Tor and Ext, joint with Ryo Takahashi; Acta Math Vietnam 47, 123–139 (2022). https://doi.org/10.1007/s40306-021-00443-0.
Complexity and rigidity of Ulrich modules, and some applications, joint with Dipankar Ghosh; MATHEMATICA SCANDINAVICA; DOI: 10.7146/math.scand.a-136499.
Splitting of morphisms induced by unit map of adjoint functors: some applications
On the projective dimension of tensor products of modules, joint with Olgur Celikbas, Toshinori Kobayashi, https://arxiv.org/abs/2304.04490.
Strong generation and (co)ghost index for module categories, joint with Pat Lank and Ryo Takahashi, https://arxiv.org/abs/2307.13675.
On containment of trace ideals in ideals of finite homological dimension; joint with Monalisa Dutta, https://arxiv.org/abs/2312.01230 .
A note on generation and descent for derived categories of noncommutative schemes, with Anirban Bhaduri and Pat Lank, https://arxiv.org/abs/2312.02840 .
Two theorems on the vanishing of Ext, joint with Olgur Celikbas, Toshinori Kobayashi, Hiroki Matsui, Arash Sadeghi, https://arxiv.org/abs/2308.08999.
On a generalized Auslander-Reiten conjecture, joint with Shinya Kumashiro, and Parangama Sarkar, https://arxiv.org/abs/2209.12718.
Some characterizations of local rings via reducing dimensions, joint with Olgur Celikbas, Toshinori Kobayashi, Hiroki Matsui, arXiv:2212.05220.
Ulrich split rings; joint with Hailong Dao and Monalisa Dutta, https://arxiv.org/abs/2210.03872.
Finite homological dimension of Hom and vanishing of Ext, joint with Dipankar Ghosh, https://arxiv.org/abs/2310.10607.
Trace ideal and annihilator of Ext and Tor of regular fractional ideals, and some applications, https://arxiv.org/abs/2210.03891.
Finite Birational extension with stable conductor, arXiv:2212.09087.
Some new invariants of Noetherian local rings related to square of the maximal ideal; joint with Dylan C. Beck; https://arxiv.org/abs/2205.01658.