Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Enumerative Combinatorics
No full textEnumerative Combinatorics focuses on the exact and asymptotic counting
of combinatorial objects. It has fruitful connections
to several disciplines, including statistical physics, algebraic
combinatorics, probability theory, graph theory and computer science. This workshop brought
together experts from all these various fields with the goal of promoting cooperation and interaction among
researchers with largely varying backgrounds.
It was the third workshop on this topic (the first two editions dating back to 2014 and 2018) and this time the main focus was on interactions with algebraic combinatorics
Characterization of Tropical Planar Curves up to Genus Six
No full textWe provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six
Birational Rowmotion on a Rectangle over a Noncommutative Ring
No full textWe extend the periodicity of birational rowmotion for rectangular posets to the case when the base field is replaced by a noncommutative ring (under appropriate conditions). This resolves a conjecture from 2014. The proof uses a novel approach and is fully self-contained
MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics
No full textThe central theme of the workshop were nonlocal operators which appear in various branches of mathematics (PDEs, fractional calculus, stochastic processes, statistics). Although the basic concepts are similar, both language and methods differ depending on one's own community. The aim of the workshop was to bring together leading researchers from these disciplines, in order to alert the different communities about the problems, methods, and progress achieved separately, and to bridge the gap caused by different background and different mathematical terminology
On the Enumeration of Finite -Algebras
No full textWe use Constraint Satisfaction Methods to construct and enumerate finite L-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang-Baxter equation. There are 377322225 isomorphism classes of -algebras of size eight. The database constructed suggest the existence of bijections between certain classes of -algebras and well-known combinatorial objects. On the one hand, we prove that Bell numbers enumerate isomorphism classes of finite linear -algebras. On the other hand, we also prove that finite regular -algebras are in bijective correspondence with infinite-dimensional Young diagrams
Diophantische Approximationen
No full textThis workshop was focused on a large variety of problems which have seen important progress during the last few years, such as extensions and refinements of Schmidt Subspace Theorem, together with new applications, works on the Zilber-Pink conjecture and on unlikely intersections, geometry of numbers, simultaneous Diophantine approximation, theory of heights, continued fractions, and arithmetic dynamics
On a Conjecture of Khoroshkin and Tolstoy
No full textWe prove a no-go theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal -matrix, yielding a negative answer to a conjecture of Khoroshkin and Tolstoy from [Lett. Math. Phys. vol. 36 1996]
Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects
No full textThe workshop covered recent developments in algebraic geometry
in a broad sense with a special emphasis on various moduli spaces.
Problems related to mirror symmetry phenomena were discussed in
a number of talks as well as singularity theory in the context of the MMP
in positive characteristic. Derived categories and algebraic cycles, as
well as rationality questions figured prominently in the talks and the discussions
Some Homological Properties of Borel Type Ideals
No full textWe study ideals of Borel type, including -Borel ideals and -spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated squarefree principal Borel ideals are computed. For the multiplicity, the result is given under an additional assumption which is always satisfied for squarefree principal Borel ideals. These results are used to analyze the behaviour of height, multiplicity and analytic spread of the homological shift ideals as functions of , when is an equigenerated squarefree
Borel ideal
The Robinson–Schensted algorithm
No full textI am going to describe the Robinson–Schensted algorithm which transforms a permutation of the numbers from 1 to n into a pair of combinatorial objects called “standard Young tableaux”. I will then say a little bit about a few of the fascinating properties of this transformation, and how it connects to current research