Related papers: Traversal-invariant characterizations of logarithm…
In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we construct in this paper, together with the ones constructed in…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
We use categorical skew Howe duality to find recursion rules that compute categorified sl(N) invariants of rational tangles colored by exterior powers of the standard representation. Further, we offer a geometric interpretation of these…
A residue-theoretic representation is given for massless matter fields in (quotients) of (weighted) \CY\ complete intersection models and the corresponding chiral operators in \LGO{s}. The well known polynomial deformations are thus…
We formalize the proof of Reingold's Theorem that SL=L [Rei05] in the theory of bounded arithmetic VL, which corresponds to ``logspace reasoning''. As a consequence, we get that VL=VSL, where VSL is the theory of bounded arithmetic for…
Notes from the report at the Fields institute in Toronto. We introduce the Donaldson-Thomas invariants and describe the wall-crossing formulas for numerical Donaldson-Thomas invariants.
Our main contributions can be divided in three parts: (1) Fixpoint extensions of first-order logic: we give a precise syntactic and semantic characterization of the relationship between $\mathrm{FO(TC^1)}$ and $\mathrm{FO(LFP)}$; (2)…
We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a…
Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed, using an abstract…
Vogan and Barbasch-Vogan attach two similar invariants to representations of a reductive Lie group, one by an algebraic process, the other analytic. They conjectured that the two invariants determine each other in a definite manner. Here we…
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
The logarithmic Laplacian on the (whole) N-dimensional Euclidean space is defined as the first variation of the fractional Laplacian of order 2s at s=0 or, alternatively, as a singular Fourier integral operator with logarithmic symbol.…
Recent progress in holographic correspondence uncovered remarkable relations between key characteristics of the theories on both sides of duality and certain integrable models. In this note we revisit the problem of the role of certain…
We give a survey of computation of the conformal capacity of planar condensers, generalized capacity, and logarithmic capacity with emphasis on our recent work 2020-2025. We also discuss some applications of our method based on the boundary…