Related papers: Towards Flying through Modular Forms
These are the lecture notes from my portion of a mini-course for the summer school "Building Bridges 3" that was held in Sarajevo during July 2016. My lectures covered the Katz definition of modular forms, a family of forms defined from…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…
The present article studies decompositions of vector bundles on the moduli stack of elliptic curves that are pushforwards of vector bundles on moduli of elliptic curves with level structure. These imply decomposition results for rings of…
Modeling has been created for a Space-to-Surface system defined for an optimal trajectory for targeting in terminal phase with avoids an intercepting process. The modeling includes models for simulation atmosphere, speed of sound,…
False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular…
Recently, the theory concerning piecewise smooth vector fields (PSVFs for short) have been undergoing important improvements. In fact, many results obtained do not have an analogous for smooth vector fields. For example, the chaoticity of…
High-quality reconstruction of controllable 3D head avatars from 2D videos is highly desirable for virtual human applications in movies, games, and telepresence. Neural implicit fields provide a powerful representation to model 3D head…
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…
In this paper, we study modular transformation properties of a certain class of functions with indefinite quadratic forms.
The task of synthesizing novel views from a single image has useful applications in virtual reality and mobile computing, and a number of approaches to the problem have been proposed in recent years. A Multiplane Image (MPI) estimates the…
In nature, the collective behavior of animals, such as flying birds is dominated by the interactions between individuals of the same species. However, the study of such behavior among the bird species is a complex process that humans cannot…
Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…
The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete…
Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…
Existing inverse physics methods recover physical parameters from multi-view videos, where geometric constraints across views resolve scale and 3D structure. In monocular settings, however, such constraints are absent, leading to severe…
This paper focuses on visual motion-based invariants that result in a representation of 3D points in which the stationary environment remains invariant, ensuring shape constancy. This is achieved even as the images undergo constant change…
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…