44 citations · 197 across the 17 of their papers we have counts for
17 papers
Nested Inductive Bias Framework for SPD Manifold Learning
Tushar Das
In Geometric Deep Learning, inductive biases serve two primary functions: enforcing manifold constraints and embedding relational priors. Currently, representation learning on SPD…
Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learning
Tushar Das, Subrata Dutta, Sarmistha Neogy +1
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features i…
Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism
Tushar Das, Lior Fishman, David Simmons +1
We consider small perturbations of a conformal iterated function system (CIFS) produced by either adding or removing some generators with small derivative from the original. We est…
On the dimension spectra of infinite iterated function systems
Tushar Das, David Simmons
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two const…
Thermodynamic formalism for coarse expanding dynamical systems
Tushar Das, Feliks Przytycki, Giulio Tiozzo +2
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discuss…
A variational principle in the parametric geometry of numbers
Tushar Das, Lior Fishman, David Simmons +1
We extend the parametric geometry of numbers (initiated by Schmidt and Summerer, and deepened by Roy) to Diophantine approximation for systems of linear forms in variables,…
Intersecting limit sets of Kleinian subgroups and Susskind's question
Tushar Das, David Simmons
We construct a non-elementary Fuchsian group that admits two non-elementary subgroups with trivial intersection and whose radial limit sets intersect non-trivially. This negatively…
A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation
Tushar Das, Lior Fishman, David Simmons +1
We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the…
Badly approximable points on self-affine sponges and the lower Assouad dimension
Tushar Das, Lior Fishman, David Simmons +1
We highlight a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of…
The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result
Tushar Das, David Simmons
We construct a self-affine sponge in whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hau…
Badly approximable vectors and fractals defined by conformal dynamical systems
Tushar Das, Lior Fishman, David Simmons +1
We prove that if is the limit set of an irreducible conformal iterated function system (with either finite or countably infinite alphabet), then the badly approximable vectors…
A proof of the matrix version of Baker's conjecture in Diophantine approximation
Tushar Das, David Simmons
We prove that the matrix analogue of the Veronese curve is strongly extremal in the sense of Diophantine approximation, thereby resolving a question posed by Beresnevich, Kleinbock…
Tukia's isomorphism theorem in CAT(-1) spaces
Tushar Das, David Simmons, Mariusz Urbański
We prove a generalization of Tukia's ('85) isomorphism theorem which states that isomorphisms between geometrically finite groups extend equivariantly to the boundary. Tukia worked…
Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems
Tushar Das, Lior Fishman, David Simmons +1
We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalize…
Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures
Tushar Das, Lior Fishman, David Simmons +1
We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalize…
Dimension rigidity in conformal structures
Tushar Das, David Simmons, Mariusz Urbański
Let be the limit set of a conformal dynamical system, i.e. a Kleinian group acting on either finite- or infinite-dimensional real Hilbert space, a conformal iterated function s…
Geometry and dynamics in Gromov hyperbolic metric spaces: With an emphasis on non-proper settings
Tushar Das, David Simmons, Mariusz Urbański
Our monograph presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Our work unifies and extends a long list of r…