Welcome to Steve Rosenberg's Home Page

Office: MCS 248
Office Hours: Monday, Wednesday, Thursday 3-4
Email: sr(at)math.bu.edu

Research

My research interests are in differential geometry in finite and infinite dimensions, particularly with applications to/from mathematical physics. Almost all this work uses Laplacian-type operators sooner or later. My current work focuses on characteristic classes for infinite dimensional bundles, with collaborations with Andres Larrain-Hubach, Yoshi Maeda, Sylvie Paycha, Simon Scott, and Fabian Torres-Ardila. Older work includes the functional/zeta determinant of Laplacians, which is a key element of quantum field theory (or non-theory), and (with K. D. Elworthy and Xue-Mei Li) applications of Brownian motion to differential geometry. This has given a series of results of the type: topological condition A on a compact manifold implies that metrics of type B cannot exist on the manifold. In particular, these theorems extend the classical Bochner and Myers type theorems. Heat operators associated to Laplacians figure heavily in this work; after all, Brownian motion is supposed to model heat flow as an example of infinite dimensional Riemannian geometry. More recently, in a series of papers with Andres Larrain-Hubach, Yoshiaki Maeda, Sylvie Paycha, Simon Scott and Fabian Torres-Ardila, we've studied primary and secondary characteristic classes on infinite dimensional manifolds such as loop spaces; here the Laplacians enter in the curvature of connections on these manifolds

Other work: Yoshiaki Maeda, Philippe Tondeur and I have worked on the geometry of the gauge orbits in the space of connections, and on the geometry of the orbits of the diffeomorphism group in the space of metrics on a manifold. Mihail Fromosu and I have studied Mathai-Quillen forms, which have formal applications in QFT and rigorous applications in differential geometry. There are also preprints on quantum cohomology (with Mihaela Vajiac), and on Lax pairs and Feynman diagrams (with Gabriel Baditoiu). Here is a list of available preprints/reprints.

Yaiza Canzani García

Department of Mathematics

Harvard University

One Oxford Street

Cambridge, MA 02138

Office # 238

Email: canzani@math.harvard.edu

My research interests are Spectral Geometry, Semiclassical Analysis and Conformal Geometry.

http://www.mathcs.emory.edu/~ono/about-me/

http://www.smp.uq.edu.au/people/PadraigOCathain/

Padraig Ó Catháin

Postdoctoral Research Fellow

School of Mathematics and Physics
The University of Queensland
St Lucia, Brisbane 4072

Office Location: 67-742
Email: p.ocathain@uq.edu.au

Research

• Preprints of papers, slides from talks I have given etc. are available here.
• Click here for details of my research interests.
• Some people may be interested in an English translation of Hadamard's 1893 paper. The key result in Section 3 is the Jacobi determinant identity, a proof which is included as a postscript.

http://www.math.dartmouth.edu/~orellana/

Rosa Orellana

   Publications and Research

http://www.math.uiuc.edu/~ford/

KEVIN FORD

Department of Mathematics, The University of Illinois at Urbana-Champaign Urbana, IL 61801
Office: 304 Altgeld Hall; (217) 265-6255
e-mail: ford(AT)math(DOT)uiuc(DOT)edu

Research

http://pages.cs.wisc.edu/~cdx/

Denis Xavier Charles 

About myself

I am a final year Ph.D. student studying Computational Number Theory here at UW under the supervision of Prof. Eric Bach . My main interests are in Theory of Computation - in particular Complexity Theory, Design and Analysis of algorithms, Combinatorics, Number Theory and Algebra.

I did my undergraduate degree at Birla Institute of Technology and Science, Pilani - INDIA. I completed my masters at University at Buffalo (SUNY) under the supervision of Ken Regan .

Karin Halupczok

Mathematisches Institut
Fachbereich Mathematik und Informatik der Universität Münster
Einsteinstraße 62
D-48149 Münster

Interests of research

Deutsche Version

• Additive number theory, especially Goldbach's problem
• Circle method, analytic number theory
• Diophantine approximations, algebraic complexity theory
• Algorithmic number theory

http://www.cs.princeton.edu/~achaney/

Allison June Barlow Chaney

I am a third year graduate student at Princeton, working with David Blei and studying machine learning.  I'm interested in recommendation systems, visualization, and online inference.

http://www.math.fsu.edu/~hironaka/

Eriko Hironaka, Professor

Research: Low-dimensional topology, Mapping class groups