Research
Research
Research
Research
453+ open-access research outputs.
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric a…
We establish formulas for the Poincar\'e polynomial of the type B analogue of the Deligne--Knudsen--Mumford moduli space of rational curves with $n$ marked points, providing type B counterparts to res…
Market-order flow in financial markets exhibits long-range correlations. This is a widely known stylised fact of financial markets. A popular hypothesis for this stylised fact comes from the Lillo-Mik…
Memory corruption attacks have been prevalent in software for a long time. Some mitigation strategies against these attacks do exist, but they are not as far-reaching or as efficient as the CHERI arch…
The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpreta…
In this paper, we study a combinatorial Ricci flow on closed pseudo $3$-manifolds $(M,\mathcal{T})$. We prove that if every edge in the triangulation $\mathcal{T}$ has valence at least $9$, then the c…
Large Language Models (LLMs) possess strong representation and reasoning capabilities, but their application to structure-based drug design (SBDD) is limited by insufficient understanding of protein s…
We study compact complex $3$-dimensional non-K\"ahler Bismut Ricci flat pluriclosed Hermitian manifolds (BHE) via their dimensional reduction to a special K\"ahler geometry in complex dimension $2$, r…
Securing low-latency I/O in commodity systems forces a fundamental trade-off: rely on the kernel's high overhead mediated interface, or bypass it entirely, exposing sensitive hardware resources to use…
The Matsushita fundamental groups of a graph $X$, denoted $\pi_1^r(X)$, are certain discrete versions of the fundamental group for topological spaces. For $r=2$, these groups have a nice combinatorial…
We consider the Kato problem and extensions for degenerate elliptic operators of arbitrary order $2m$ ($m\geq 1$), whose coefficients are measurable, complex-valued and satisfy the G$\mathring{a}$rdin…
The class of the fine moduli space of stable $n$-pointed curves of genus zero, $\overline{\mathcal{M}_{0,n}}$, in the Grothendieck ring of varieties encodes its Poincar\'e polynomial. Aluffi-Chen-Marc…
We study the Hilbert series for $5d$ Superconformal Field Theories (SCFTs) engineered by Generalized Toric Polygons (GTPs), which extend the geometric realization of these theories from toric Calabi-Y…
In the early 2000s, Frigerio, Martelli, and Petronio studied $3$-manifolds of smallest combinatorial complexity that admit hyperbolic structures. As part of this work they defined and studied the clas…
The article (Gauge networks in noncommutative geometry, J. Geom. Phys. 75 : 71--91, 2014) that motivates this comment provides, in particular, one answer to the following natural question: what is non…
We present Marcel, a lightweight and open-source conversational agent designed to support prospective students with admission-related inquiries. The system aims to provide fast and personalized respon…
We consider random walks on ``balanced multislices'' of any ``grid'' that respects the ``symmetries'' of the grid, and show that a broad class of such walks are good spectral expanders. (A grid is a s…
Following Cornelissen, Li, Marcolli, and Smit, this short paper proves that the field structure of a number field $K$ can be reconstructed from the pair $(DR_K, I_K)$ of the Deligne-Ribet monoid $DR_K…
The widespread deployment of embedded systems in critical infrastructures, interconnected edge devices like autonomous drones, and smart industrial systems requires robust security measures. Compromis…
The celebrated Ore-DeMillo-Lipton-Schwartz-Zippel (ODLSZ) lemma asserts that n-variate non-zero polynomial functions of degree d over a field $\mathbb{F}$ are non-zero over any "grid" $S^n$ for finite…
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