Research
Research
Research
Research
255+ open-access research outputs.
We give a new definition -- and in some cases, a new construction -- of integral canonical models of Shimura varieties that uses the notion of an aperture appearing in work of Gardner--Madapusi on som…
We study Euclidean $k$-Means under the Massively Parallel Computation (MPC) model, focusing on the \emph{fully-scalable} setting. Our main result is a fully-scalable $O((\log n/\log\log n)^2)$-approxi…
Nepal Bhasha (Newari), an endangered language of the Kathmandu Valley, remains digitally marginalized due to the severe scarcity of annotated speech resources. In this work, we introduce Nw\=ach\=a Mu…
We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation $\sigma_2/\sigma_1=1$ in $\mathbb{R}^n$. The proof is based on the observation that after rewriting the quoti…
When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of $\mathrm{GL}_2 \times \mathrm{GL}_1$ on the space of polynomials of degree $…
For any prime $p>0$, we prove that simple superspecial abelian surfaces over $\mathbb{F}_{p}$ admit CM liftings after base change at most to $\mathbb{F}_{p^2}$, by using the residual reflex condition …
Due to any toroidal current column, the magnetic field is found to be sensitive as well as insensitive to its cross-sectional area depending on location of subject point, as predicted by numerical app…
A recent work of Goyal, Harsha, Kumar and Shankar gave nearly linear time algorithms for the list decoding of Folded Reed-Solomon codes (FRS) and univariate multiplicity codes up to list decoding capa…
In $2020$, Bhargava, Shankar, Taniguchi, Thorne, Tsimerman, and Zhao proved that for a finite extension $K/\mathbb{Q}$ of degree $n\geq 5$, the size of the $2$-torsion class group is bounded by $\# h_…
How to arrive at the densest matter in massive compact stars starting from Walecka's linear $\omega$-$\sigma$ mean-field model is described in a series of arguments anchored on hidden local symmetry, …
In this paper, we report the results of the TeamNRC's participation in the BHASHA-Task 1 Grammatical Error Correction shared task https://github.com/BHASHA-Workshop/IndicGEC2025/ for 5 Indian language…
We study the low-lying zeros of certain Artin $L$-functions associated with $D_4$-quartic function fields. Specifically, we prove that when ordered by conductor, at least $77\%$ of these $L$-functions…
As is well known, the chiral Gross-Neveu model at finite density can be solved semi-classically with the help of the chiral spiral mean field. The fermion spectrum has a single gap right at the Fermi …
Preliminary astrometric data from the fourth data release of the $Gaia$ mission revealed a 33 M$_{\odot}$ dark companion to a metal-poor red giant star, deemed $Gaia$ BH3. This system hosts both the m…
This paper introduces Bhasha-Rupantarika, a light and efficient multilingual translation system tailored through algorithm-hardware codesign for resource-limited settings. The method investigates mode…
Given a $(0,p)$-mixed characteristic complete discrete valued field $\mathcal{K}$ we define a class of finite field extensions called \emph{pseudo-perfect} extensions such that the natural restriction…
We study several rigidity properties of $p$-adic local systems on a smooth rigid analytic space $X$ over a $p$-adic field. We prove that the monodromy of the log isocrystal attached to a $p$-adic loca…
The complexity of representing a polynomial by a Read-Once Oblivious Algebraic Branching Program (ROABP) is highly dependent on the chosen variable ordering. Bhargava et al. prove that finding the opt…
We study notions of conjugate points along timelike geodesics in the synthetic setting of Lorentzian (pre-)length spaces, inspired by earlier work for metric spaces by Shankar--Sormani. After prelimin…
Rapid developments of large language models have revolutionized many NLP tasks for English data. Unfortunately, the models and their evaluations for low-resource languages are being overlooked, especi…
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