Related papers: Geometrization of Trace Formulas
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…
We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in…
Computing the crossing number of a graph is one of the most classical problems in computational geometry. Both it and numerous variations of the problem have been studied, and overcoming their frequent computational difficulty is an active…
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…
Developing and maintaining CLP programs requires visualization and explanation tools. However, existing tools are built in an ad hoc way. Therefore porting tools from one platform to another is very difficult. We have shown in previous work…
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating…
In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous,…
We conjecture and prove closed-form index expressions for the cohomology dimensions of line bundles on del Pezzo and Hirzebruch surfaces. Further, for all compact toric surfaces we provide a simple algorithm which allows expression of any…
The note provides a description of the homology of $GL_3$ over function rings of affine elliptic curves over arbitrary fields, following the earlier work of Takahashi and Knudson in the case $GL_2$. Some prospects for applications to…
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with binary coplanarity relation, as well as with binary relation of being in one pencil of lines, is a sufficient…
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
We study hyperbolic curves and their Jacobians over finite fields in the context of anabelian geometry.
We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. Under…