相关论文: What Juris Hartmanis taught me about Reductions

Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by…

This texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions…

A few remarks on integrable dynamical systems inspired by discussions with Jurgen Moser and by his work.

In order to model an efficient learning paradigm, iterative learning algorithms access data one by one, updating the current hypothesis without regress to past data. Past research on iterative learning analyzed for example many important…

This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…

I will share with the reader what I have learned from Richard Stanley and the ways in which he has contributed to research in combinatorics conducted by me and my collaborators.

Over the past 20 years, a great deal of work has been done on the moduli spaces of coherent systems on algebraic curves. Until recently, however, there has been very little work on the fixed determinant case, except for the special case of…

Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…

These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…

Inspired by the work of L. Drewnowski in [Studia Math. 77 (1984) 373--391], our research reveals new insights and characterizes the notion of spaceability in the context of complements of subspaces (not necessarily closed) within the…

In these lectures we give an introduction to the reduction theory of binary forms starting with quadratic forms with real coefficients, Hermitian forms, and then define the Julia quadratic for any degree $n$ binary form. A survey of a…

Embeddings play a pivotal role across various disciplines, offering compact representations of complex data structures. Randomized methods like Johnson-Lindenstrauss (JL) provide state-of-the-art and essentially unimprovable theoretical…

This paper fixes a gap in my article "Support varieties of non-restricted modules over Lie algebras of reductive groups" pointed out to me by J.C. Jantzen. It was written several years ago, but never widely circulated.

We study a notion of dimension which was introduced by R. Heitmann in his remarkable paper in 1984, and also a related notion, implicit in the proofs in his paper. We develop these notions in the general framework of distributive lattices…

The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.

Reductionism has dominated science and philosophy for centuries. Complexity has recently shown that interactions---which reductionism neglects---are relevant for understanding phenomena. When interactions are considered, reductionism…

This note records some dilation theorems about contraction semigroups on a Hilbert space - all of which fall into the categories "known" or "probably known" - that I proved while working on my PhD in mathematics (under the supervision of…

This paper agrees basically with the talk of the author at the workshop "Homological Mirror Symmetry and Applications", Institute for Advanced Study, Princeton, March 2007.

Here we survey the compactness and geometric stability conjectures formulated by the participants at the 2018 IAS Emerging Topics Workshop on {\em Scalar Curvature and Convergence}. We have tried to survey all the progress towards these…

The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…