Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
Not a member yet
2063 research outputs found
Sort by
Tropical and Logarithmic Methods in Enumerative Geometry
No full textThis book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations
The Brown Complex in Non-Defining Characteristic and Applications
No full textWe study the Brown complex associated to the poset of -subgroups in the case of a finite reductive group defined over a field of characteristic prime to . First, under suitable hypotheses, we show that its homotopy type is determined by the generic Sylow theory developed by Broué and Malle and, in particular, only depends on the multiplicative order of modulo . This result leads to several interesting applications to generic Sylow theory, mod homology decompositions, and -modular representation theory. Then, we conduct a more detailed study of the Brown complex in order to establish an explicit connection between the local-global conjectures in representation theory of finite groups and the generic Sylow theory. This is done by isolating a family of -subgroups of finite reductive groups that corresponds bijectively to the structures controlled by the generic Sylow theory.I would like to thank Francesco Fumagalli for some comments on an earlier version of this paper and Gunter Malle for a thorough reading of the material presented here and for pointing out some inaccuracies. This work was initiated during a visit of the author to the University of Florence and then completed during a stay at the Mathematisches Forschungsinstitut Oberwolfach funded by a Leibniz Fellowship. I am grateful to both institutions for their hospitality and support
Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory
No full textThe workshop "Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory" covered interactions between geometric problems involving fractals, dimensions, patterns, projections and incidences, and on the other hand recent developments in Fourier analysis and Ergodic theory which have been inspired by fractal geometric problems, or have been instrumental in solving them
Group Actions and Harmonic Analysis in Number Theory
No full textThis workshop focuses on new problems and new methods at the interface of harmonic analysis (taken in a very broad sense) and ergodic theory, with applications focused on number theory. Special emphasis is put on equidistribution problems on arithmetic symmetric spaces, effective methods in homogeneous dynamics, periods of automorphic forms, families of -functions over number fields and function fields, and applications of Fourier uniqueness
Mathematical Logic: Proof Theory, Constructive Mathematics
No full textThe Workshop "Mathematical Logic: Proof Theory,
Constructive Mathematics" focused on proof-theoretic research on
the foundations of mathematics, on
the extraction of explicit computational content from
given proofs in core areas of ordinary mathematics using proof-theoretic
methods as well as on topics in proof complexity.
The workshop contributed to the following research strands:
interactions between foundations and applications,
proof mining,
constructive and semi-constructive reasoning,
proof theory and theoretical computer science,
structural proof theory
Representation Theory of Quivers and Finite-Dimensional Algebras
No full textThis workshop was about the representation theory of quivers and finite-dimensional (associative) algebras, and links to other areas of mathematics, including other areas of representation theory, homological algebra, cluster algebras, algebraic geometry and singularity theory. Particularly active topics included -tilting theory, algebras arising from surface triangulations and the study of exact categories and their generalizations
Real Enumerative Invariants Relative to the Anti-Canonical Divisor and their Refinement
No full textWe introduce new invariants of the projective plane (and, more generally, of
certain toric surfaces) that arise from the appropriate enumeration of real
elliptic curves. These invariants admit a refinement (according to the quantum
index) similar to the one introduced by Grigory Mikhalkin in the rational case.
We also construct tropical counterparts of the refined elliptic invariants
under consideration and establish a tropical algorithm allowing one to compute,
a suitable version of the correspondence theorem, the above
invariants
Tomographic Inverse Problems: Mathematical Challenges and Novel Applications
No full textThis workshop brought together researchers working on
mathematical problems related to tomography, with a particular
emphasis on novel applications and associated mathematical challenges.
Examples of respective issues represented in the workshop were
tomographic imaging with Compton cameras or coupled-physics imaging,
resolution and aliasing, vector and tensor field tomography,
diffraction tomography, magnetic particle tomography, and limited data, all of which are motivated by the many modern
applications. These topics were complemented by novel algorithmic
strategies in the solution of tomographic inverse problems, such as
stochastic methods and machine learning techniques. Bringing together
mathematical and scientific researchers working on these different
mathematical problems created a fruitful interchange with novel ideas
and strong impact for the future of the field
Mini-Workshop: Mathematics of Many-body Fermionic Systems
No full textFermionic quantum systems are well described by the linear many-body Schrödinger equation. For interacting systems the full Schrödinger theory is extremely complicated and theoretical as well numerical investigations are not feasible. In practice, macroscopic properties of large systems can therefore only be accessed by means of approximate theories. The intention of this workshop was to showcase the most recent advances in the mathematical study of many-body interacting fermionic systems and to stimulate discussions among different research groups
Mini-Workshop: Homological Aspects for TDLC-Groups
No full textThis mini-workshop aimed at bringing together experts and early career researchers on finiteness conditions for discrete groups, and experts on varying aspects of locally compact groups to find a common framework to develop a systematic theory of homological finiteness conditions for totally disconnected locally compact groups. Whereas the homological theory of
finiteness conditions of discrete groups is well developed and the structure theory of totally disconnected locally compact
groups has seen some important breakthroughs in the last decade, the homological theory for (non-compact) totally disconnected locally compact groups is an emerging research area. Specific
topics include finiteness conditions for locally compact groups, Mackey functors
and Bredon cohomology for topological groups, connections to condensed mathematics, connections to -invariants and -invariants