arXiv research

Describes automorphism group of Rauzy diagrams.

Abstract compares two norms in holomorphic quadratic differentials.

We give a new description of the Arnoux-Yoccoz mapping classes as a product of two Dehn twists and a finite order element. The construction is analogous to Penner's construction of mapping classes with small stretch factors.

We present a new description of the genus 3 Arnoux--Yoccoz translation surface in terms of its Delaunay polygons and show that, up to affine equivalence, it belongs to two families of surfaces whose isometry groups include the dihedral group of the square.

The family of translation surfaces $(X_g,ω_g)$ constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus $g$ greater than or equal to $3$. We triangulate these surfaces and deduce general properties they share. The surfaces $(X_g,ω_g)$ converge to a surface $(X_\i…

We prove that the Teichmueller disc stabilized by the Arnoux-Yoccoz pseudo-Anosov diffeomorphism contains at least two closed Teichmueller geodesics. This proves that the corresponding flat surface does not have a cyclic Veech group. In addition, we prove that this Teichmueller disc is dense inside the hyperelliptic lo…

We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy Cantor sets, and prove that any two such objects in the plane are ambiently homeo…

Study conjugacy classes of parabolic diffeomorphisms fixing the origin.

Classifies GL(2,R)-invariant subvarieties in complex geometry.

Study of origamis in minimal stratum with single cylinders, calculating spin parities and monodromy groups.

Study of translation covers of platonic solids reveals monodromy group structures.

Connectedness proved for $\mathbb{Z}^d$ actions on 1D manifolds by $C^2$ diffeomorphisms.

We consider in this paper some structured financial products, known as reverse convertible notes, that resulted in substantial losses to certain buyers of these notes in recent years. We shall focus on specific reverse convertible notes known as "Autocallable Optimization Securities with Contingent Protection Linked to…

Lecture notes on Finslerian geometry.

Study finds limit points of bass notes on hyperbolic surfaces.

Explains the Schwarz lemma in lecture notes.

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A number of people, both in and out of the class, found these notes very useful and so …

Lecture notes introduce differential geometry using sheaves and differential operators.

Lecture note for data science students on machine learning basics and advanced topics.

Lecture notes on advanced geometry equations and subvarieties.

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.

Study spectral gaps and bass notes of random hyperbolic 3-orbifolds.

Notes for a one semester course. The notes contain a description of compact three dimensional Seifert fibered spaces and a classification up to homeomorphism of compact three dimensional Seifert fibered spaces with non-empty boundary.

These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to "String Topology" and cacti are announced in Section 2.7.

In this note, we prove an index theorem on Galois covering for Heisenberg elliptic differential operators, which is not elliptic, analogous to Atiyah's $Γ$-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial $Γ$-index.

Patient summarization is essential for clinicians to provide coordinated care and practice effective communication. Automated summarization has the potential to save time, standardize notes, aid clinical decision making, and reduce medical errors. Here we provide an upper bound on extractive summarization of discharge …

Lecture notes on curves in complex projective plane from a topological viewpoint.

Notes describe geometric interpretations of cohomology in trisected 4-manifolds.

This note comprises a negative resolution of the Efficient Market Hypothesis.

These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this rapidly growing field. The notes are the basis of lectures given at the conference…

This note is devoted to partial study of recurrent equation $dω=β\wedge ω$, based on linear algebra of exterior forms. Such equation was considered by Lee, for non-degenerate 2-form. In this note we approach general case, when $ω$ is arbitrary. Particularly, we extend results obtained by Lee, on odd-forms.

These are notes on some algebraic geometry of complex projective curves, together with an application to studying the contact curves in CP^3 and the null curves in the complex quadric Q^3 in CP^4, related by the well-known Klein correspondence. Most of this note consists of recounting the classical background. The main…

Abstract notes on generative modeling techniques.

A note on setting swap parameters for traders.

This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.

Lecture notes on Heegaard Floer homology for 3-manifolds and knots.

Health professionals can use natural language processing (NLP) technologies when reviewing electronic health records (EHR). Machine learning free-text classifiers can help them identify problems and make critical decisions. We aim to develop deep learning neural network algorithms that identify EHR progress notes perta…

In this note we show that Lorentzian Concircular Structure manifolds (LCS)_n coincide with Generalized Robertson-Walker space-times.

Clinical notes in electronic health records contain highly heterogeneous writing styles, including non-standard terminology or abbreviations. Using these notes in predictive modeling has traditionally required preprocessing (e.g. taking frequent terms or topic modeling) that removes much of the richness of the source d…

BERT-XML automates ICD coding from EHR notes using BERT pretraining.

Note refutes examples of Landsberg surfaces with vanishing flag curvature.

Paper introduces methods to automatically generate SOAP notes from patient-physician conversations.

In these notes we give an interdisciplinary result which links the geometric concept of minimal surfaces with generalized harmonic functions.

Notes on relative algebroids for geometric problems.

These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.

In this note, we prove the regularity of eta forms by the Clifford asymptotics. Then we generalize this result to the equivariant case.

In this note we construct infinitely many distinct simply connected Stein fillings of a certain infinite family of contact 3--manifolds.

In this note we prove that for a Riemannian manifold the Osserman pointwise condition is equivalent to the Rakić duality principle.