Download or read book Quiver Grassmannians of Extended Dynkin Type D written by Oliver Lorscheid and published by . This book was released on 2019 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let Q be a quiver of extended Dynkin type \widetildeD}_n. In this first of two papers, the authors show that the quiver Grassmannian \mathrmGr}_{underline{e}}(M) has a decomposition into affine spaces for every dimension vector underlinee} and every indecomposable representation M of defect -1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of \mathrmGr}_{underline{e}}(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.

Download or read book Quiver Grassmannians of Extended Dynkin Type D Part I Schubert Systems and Decompositions into Affine Spaces written by Oliver Lorscheid and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.

Download or read book Quiver Grassmannians of Extended Dynkin Type D written by Oliver Lorscheid and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Representation Theory and Beyond written by Jan Šťovíček and published by American Mathematical Soc.. This book was released on 2020-11-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Download or read book Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type written by Carles Broto and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG∧p in terms of Out(G).

Download or read book The Mother Body Phase Transition in the Normal Matrix Model written by Pavel M. Bleher and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this present paper, the authors consider the normal matrix model with cubic plus linear potential.

Download or read book Affine Flag Varieties and Quantum Symmetric Pairs written by Zhaobing Fan and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.

Download or read book Degree Theory of Immersed Hypersurfaces written by Harold Rosenberg and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.

Download or read book Subgroup Decomposition in Out Fn written by Michael Handel and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work the authors develop a decomposition theory for subgroups of Out(Fn) which generalizes the decomposition theory for individual elements of Out(Fn) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

Download or read book The Triangle Free Process and the Ramsey Number R 3 k written by Gonzalo Fiz Pontiveros and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the “diagonal” Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the “off-diagonal” Ramsey numbers R(3,k). In this model, edges of Kn are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted Gn,△. In 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that R(3,k)=Θ(k2/logk). In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.

Download or read book Global Well Posedness of High Dimensional Maxwell Dirac for Small Critical Data written by Cristian Gavrus and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors prove global well-posedness of the massless Maxwell–Dirac equation in the Coulomb gauge on R1+d(d≥4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell–Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell–Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell–Dirac takes essentially the same form as Maxwell-Klein-Gordon.

Download or read book Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees written by Rodney G. Downey and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.

Download or read book A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree Depth written by Jaroslav Nešetřil and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.

Download or read book The Bounded and Precise Word Problems for Presentations of Groups written by S. V. Ivanov and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.

Download or read book Localization for THH ku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories written by Andrew J. Blumberg and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.

Download or read book Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation written by Victor Beresnevich and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Complex Analytic Methods in the Study of Non Orientable Minimal Surfaces in Rn written by Antonio Alarcón and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.