A5064610434- Geometric and Algebraic Topology
- Homotopy and Cohomology in Algebraic Topology
- Algebraic Geometry and Number Theory
- Mathematical Dynamics and Fractals
- Advanced Combinatorial Mathematics
- Algebraic structures and combinatorial models
- Mathematics and Applications
- Advanced Topics in Algebra
- Topological and Geometric Data Analysis
- Protein Structure and Dynamics
- RNA and protein synthesis mechanisms
- Analytic and geometric function theory
- History and Theory of Mathematics
- Organometallic Compounds Synthesis and Characterization
- Amyloidosis: Diagnosis, Treatment, Outcomes
- Cerebrovascular and genetic disorders
- Advanced Algebra and Geometry
- Advanced Algebra and Logic
- Advanced Numerical Analysis Techniques
- Rings, Modules, and Algebras
- RNA Research and Splicing
- Geometric Analysis and Curvature Flows
- Geometry and complex manifolds
- SARS-CoV-2 and COVID-19 Research
- Nonlinear Waves and Solitons
Institut des Hautes Études Scientifiques
2016-2025
University of California, Los Angeles
1993-2021
California Institute of Technology
2011-2017
Aarhus University
2008-2017
University of Southern California
2003-2017
Schrodinger (United States)
2017
University of Vienna
2017
University of Southern Denmark
2011
University of Kaiserslautern
2011
University of Copenhagen
2011
2g)! for s ^ 1, g > 0, and 2g -2 + where B denotes the 2gth Bernoulli number.This result is proved by Harer Zagier [5] using computational techniques (rediscovered in [5]) which are related to perturbative series of quantum field theory (see [2] §2 below).Herein, we apply a variant full machine capture equivariant combinatorics certain cell decompositions foliated fiber bundles over various Teichmuller spaces.In contrast, begins with spaces themselves, only part machinery applicable
In this paper, we introduce a method for dividing up noncompact hyperbolic manifold of finite volume into canonical Euclidean pieces.The construction first arose in the setting surfaces (see [7]), and case one gets cell decomposition surface structure.(The structure, course, is not complete.)The conformal structure underlying does agree with but two structures are probably too distant (cf.Sullivan's theorem [5] an analogous result).This investigation from attempt to understand coordinates...
We describe a generalization of Thurston’s original construction pseudo-Anosov maps on surface <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> negative Euler characteristic. In fact, we construct whole semigroups by taking appropriate compositions Dehn twists along certain...
An explicit method of integration top-dimensional differential forms over the moduli spaces punctured Riemann surfaces is presented.This applied to computation Weil-Petersson volumes spaces, and we find that volume for twice-punctured torus π 4 /8 that, large g , once-punctured surface genus at least g~2c~2 (2g)\, where c < .15 a constant independent .Our methods depend upon certain bundle (introduced earlier) classical Teichmuller space surfaces, some our computations rely on standard...
We consider the collection of all pseudo-Anosov homeomorphisms on a surface fixed topological type. To each such homeomorphism is associated real-valued invariant, called its dilatation (which greater than one), and we define spectrum to be logarithms dilatations maps supported surface. The natural object study from topological, geometric, dynamical points view. are concerned in this paper with least element spectrum, explicit upper lower bounds derived terms type surface; train tracks main...
Abstract Motivation: Several dynamic programming algorithms for predicting RNA structures with pseudoknots have been proposed that differ dramatically from one another in the classes of considered. Results: Here, we use natural topological classification terms irreducible components are embeddable surfaces fixed genus. We add to conventional secondary four building blocks genus order construct certain arbitrarily high A corresponding unambiguous multiple context-free grammar provides an...
Abstract We introduce a new model of proteins that extends and enhances the traditional graphical representation by associating combinatorial object called fatgraph to any protein based upon its intrinsic geometry. Fatgraphs can easily be stored manipulated as triples permutations, these methods are therefore amenable fast computer implementation. Applications include refinement structural classifications prediction geometric other properties from their chemical structures. © 2010 Wiley...
Let M be a closed oriented smooth surface of genus g > 2, and let Jf ^ denote the space equivalence classes measured foliations on M. The importance began with Thurston's work diffeomorphisms surfaces: he defined Jt'J** recognized natural action mapping class group Jί3P as an extension this Teichmijller In these investigations, there arose concept pseudo-Anosov map which fixes pair transverse projective foliation M, question evolves recognizing fixed by some map.Our main result provides...
Introduction.Let F 8 denote the oriented genus g surface with s punctures, 2g -2 + s>0, s>l, and choose a distinguished puncture P of F*.Let Tg be Teichmüller space conformai classes complete finitearea metrics on F* (see [A]), let MC 9 mapping class group orientation-preserving difFeomorphisms (fixing P) modulo isotopy [B]).When 0, are understood, we omit their mention.In §1 §2, report joint work D. B. A. Epstein [EP] where new useful coordinates T given (Theorem 2) MC^-equivariant cell...
We introduce coordinates for a principal bundle S T (F ) over the super Teichmüller space ST of surface F with s ≥ 1 punctures that extend lambda length on decorated = × R + usual ).In effect, action Fuchsian subgroup P SL(2, R) Minkowski 2,1 is replaced by OSp(1|2) 2,1|2 , where denotes orthosymplectic Lie supergroup, and lengths are extended fermionic invariants suitable triples isotropic vectors in .As bosonic case, there analogue Ptolemy transformation now both even odd as well an...
This paper extends the decorated Teichmüller theory developed before for punctured surfaces to setting of "bordered" surfaces, i.e., with boundary, and there is non-trivial new structure discovered.Beyond this, main result this identifies an open dense subspace arc complex a bordered surface up proper homotopy equivalence certain quotient moduli space, namely, by natural action positive reals homothety on hyperbolic lengths geodesic boundary components.One tool in proof homeomorphism between...
Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced studied. The spaces underlying the basic operad identified with open subsets a compactification due to Penner space closely related Riemann's moduli space. Algebras over these shown be Batalin-Vilkovisky algebras, where entire BV structure is realized simplicially. Furthermore, our contains cacti up homotopy, it similarly acts loop any New structures circle...
We describe a generalization of Thurstonâs original construction pseudo-Anosov maps on surface $F$ negative Euler characteristic. In fact, we construct whole semigroups by taking appropriate compositions Dehn twists along certain families curves; our arguments furthermore apply to give examples nonorientable surfaces. For each self-map $f:F \to F$ arising from recipe, an invariant "bigon track" (a slight train track) whose incidence matrix is Perron-Frobenius. Standard produce projective...