Research
I am a Postdoctoral fellow in the Department of Algebra at Charles University, Prague, https://www.mff.cuni.cz/cs/fakulta/organizacni-struktura/lide?hdl=17181. I received my PhD from University of Kansas, USA, under the supervision of Professor Hailong Dao, in Summer 2023.
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.
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.