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There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological…

We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated…

I developed the lecture notes based on my ``Linear Model'' course at the University of California, Berkeley over the past ten years. This book provides an intermediate-level introduction to the linear model. It balances rigorous proofs and…

This volume contains the proceedings of the Workshop on Partiality and Recursion in Interactive Theorem Provers (PAR 2010) which took place on July 15 in Edinburgh, UK. This workshop was held as a satellite workshop of the International…

This volume contains the proceedings of MARS 2020, the fourth workshop on Models for Formal Analysis of Real Systems held as part of ETAPS 2020, the European Joint Conferences on Theory and Practice of Software. The MARS workshop brings…

This volume constitutes the proceedings of LFMTP 2015, the Tenth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, held on August 1st, 2015 in Berlin, Germany. The workshop was a one-day satellite event…

We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.

These are the notes from a survey talk given at Arbeitstagung 2001 covering the author's work with Lev Borisov and Sorin Popescu on toric varieties, modular forms, and equations of modular curves.

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in…

Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance…

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…

Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…

In this revised version, we add some expository material and references and make some minor corrections.

In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…

Internet topology analysis has recently experienced a surge of interest in computer science, physics, and the mathematical sciences. However, researchers from these different disciplines tend to approach the same problem from different…

This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June…

The report is based on an extended abstract for the MFO workshop "Hilbert Complexes: Analysis, Applications, and Discretizations", held at Oberwolfach during 19-25 June 2022. The aim is to provide an overview of some aspects of…

These are the lecture notes from my portion of a mini-course for the summer school "Building Bridges 3" that was held in Sarajevo during July 2016. My lectures covered the Katz definition of modular forms, a family of forms defined from…