On The Geometry Of Toric Arrangements

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FAITHFUL TROPICALIZATION OF HYPERTORIC VARIETIES

admits a natural tropicalization, induced by its embedding in a Lawrence toric variety. In this thesis, we explicitly describe the polyhedral structure of this tropicalization and calculate the bers of the tropicalization map. Using a recent result of Gubler, Rabino , and Werner, we prove that there is a continuous section of the

Laura Starkston - math.ucdavis.edu

Oct 05, 2017 smoothed toric divisors. arXiv:2012.08666 [math.SG]. Olga Plamenevskaya and Laura Starkston Unexpected Stein llings, rational surface singu-larities, and plane curve arrangements. arXiv:2006.06631 [math.GT]. Peter Lambert-Cole, Je rey Meier, and Laura Starkston. Symplectic 4-manifolds admit Weinstein trisections.

arXiv:1404.1665v1 [math.CO] 7 Apr 2014

for toric line arrangements in [11]. See also [12] for arrangements in hyperbolic spaces, icosahedron and also arrangements of immersed circles in surfaces. The aim of this paper is to give a characterization of the f-vector for toric arrangements in a 2-torus. The paper is organized as follows.

Algebra and Geometry of Con guration Spaces and related

A Tutte polynomial for toric arrangements A toric arrangement is a nite family of hypersurfaces in a torus, every hypersurface being the kernel of a character. We describe some properties of such arrangements, and we compare them with hyperplane arrangements. The Tutte polinomial is an

Michael DiPasquale

15. The Toric Ring of a Two-Borel ideal is Koszul 01/2018 AMS-MAA Joint Mathematics Meetings, San Diego, CA AMS Special Session on Combinatorial Commutative Algebra and Polytopes 16. Freeness of Multi-Coxeter Arrangements of type A 09/2017 AMS Sectional Meeting, Denton, TX Special Session on Algebraic Combinatorics of Flag Varieties 17.

Nicholas Proudfoot { Curriculum Vitae

AMS special session on Toric Geometry, Northeastern, 2018 AMS special session on Arrangements of Hypersurfaces, Northeastern, 2018 Algebra and Geometry Seminar, University of Toronto, 2018 Algebraic Geometry Seminar, University of British Columbia, 2018 Algebraic Geometry Seminar, U.C. Davis, 2017

CURRICULUM VITAE FOR HENRY K. SCHENCK EDUCATION

11. PI-NSA grant (Toric varieties, hyperplane arrangements, splines), $56,150, 2011-2013. 12. PI-NSF conference grant (Syzygies in Berlin), $20,000, 2013.

CURRICULUM VITAE FOR HENRY K. SCHENCK EDUCATION PROFESSIONAL

6. PI-MFO conference grant (Toric geometry), 2016. 7. PI-NSF grant (Systemic risk and topology), $135,000, 2013-2016 (R. Sowers co-PI). 8. PI-Fulbright grant (Multigraded algebra and surface modeling), 2014. 9. PI-BIRS conference grant (Symbolic computation and geometric modeling), 2014. 10. PI-MFO conference grant (Splines and algebraic

CHARACTERISTIC QUASI-POLYNOMIALS OF INTEGRAL HYPERPLANE

The set Aalso defines the toric arrangement A(S1) in the torus (S1) On the geometry of toric arrangements. Transform. Groups, 10(3-4):387

Christin Bibby - New AMS and AWM Fellows LSU Math

2019 Toric Arrangements, 7 lectures at CIMPA Research School on Hyperplane Arrangements (Hanoi, Vietnam). Invited conference talks 2019 Hyper JARCS: Hyperplane Arrangements and the Japanese Australian Real and Complex Singularities conference (Tokyo, Japan). AlGeCom: Algebra, Geometry, and Combinatorics Day (Washington University in St

Christopher Eur Curriculum Vitae

Advisor: David Eisenbud, Thesis: The Geometry of Divisors on Matroids Aug 2011 May 2015 Harvard University, B.A. in mathematics. Advisor: Melody Chan, Thesis: A Brief Introduction to Toric Varieties Research Interests The interplay between algebraic geometry and combinatorics. Publications Free resolutions of function classes via order

Oriented Matroids from Triangulations of d-1n-1

Algebraic Geometry: toric Hilbert schemes, Schubert calculus Tropical Geometry: tropical convexity, Stiefel tropical linear spaces Optimization: tropical linear programming, mean payo game Tropical pseudohyperplane arrangements, tropical oriented matroids, trianguloids, etc Reason II: Correct direction in view of [Sturmfels{Zelevinsky].

A survey of hypertoric geometry and topology

Just as the geometry and topology of toric varieties is deeply connected to the combinatorics of polytopes, hypertoric varieties interact richly with the combinatorics of hyperplane arrangements and matroids. Furthermore, just as in the toric case, the flow of information goes in both directions.

Arithmetic matroids and Tutte polynomials

a finitely generated abelian group. We study the representability of its dual, and, guided by the geometry of toric arrangements, we give a combinatorial interpretation of the associated arithmetic Tutte polynomial, which can be seen as a generalization of Crapo s formula. R´esum ´e.

Arithmetic matroids, Tutte polynomial, and toric arrangements

Guided by the geometry of generalized toric arrangements, w e provide a combi- natorial interpretation of the associated arithmetic Tutt e polynomial, which can be seen as a generalization of Crapo's formula for the classica l Tutte polynomial.

Zonotopes, toric arrangements, and generalized Tutte polynomials

faces in Tobtained by taking the kernel of each element of the list X. To understand the geometry of this toric arrangement one needs to describe the poset C(X) of the layers, i.e. connected components of the intersections of the hypersurfaces ([5], [9], [15], [18]). Clearly this poset depends also on the arithmetics 1365 8050

Likelihood Geometry - University of Michigan

favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. This article represents the lectures given by the second author at the CIME-

Combinatorial Convexity and Algebraic Geometry

7. Zonotopes and arrangements of hyperplanes 138 V. Lattice polytopes and fans 143 1. Lattice cones 143 2. Dual cones and quotient cones 148 3. Monoids 154 4. Fans 158 5. The combinatorial Picard group 167 6. Regulär stellar Operations 179 7. Classification problems 186 8. Fano polytopes 192 Part 2 Algebraic Geometry VI. Toric varieties 199 1.

www.matfis.uniroma3.it

Introduction A toric arrangement is a nite family of hypersurfaces in a complex torus T, each hypersurface being the kernel of a character of T. Although similar arrangements appe

Northeastern University

Mathematisches Forschungsinstitut Oberwolfach Report No. 2/2018 DOI: 10.4171/OWR/2018/2 Topologyof Arrangements and Representation Stability Organised by Graham Denham, London ON

CURRICULUM VITAE FOR HENRY K. SCHENCK EDUCATION

CURRICULUM VITAE FOR HENRY K. SCHENCK Department of Mathematics University of Illinois Urbana, Illinois 61801 EDUCATION Ph.D., Mathematics, Cornell University, 1997

A TUTTE POLYNOMIAL FOR TORIC ARRANGEMENTS

taking the kernel of each element of X. To understand the geometry of this toric arrangement one needs to describe the poset C(X) of the layers , i.e. connected components of the intersections of the hypersurfaces ([8], [12], [19], [21]). Clearly this poset also depends on the arithmetics of X , and not only on its linear algebra:

arXiv:1105.3220v3 [math.CO] 24 Jul 2011

Guided by the geometry of generalized toric arrangements, we provide a combi- natorial interpretation of the associated arithmetic Tutte polynomial, which can be seen as a generalization of Crapo s formula for the classical Tutte polynomial.

Zonotopes, toric arrangements, and generalized Tutte polynomials

TU Berlin) Zonotopes, toric arrangements, and generalized Tutte polynomialsSan Francisco, August 2010 3 / 13 Complex hyperplane arrangements If V = C n , removing hyperplanes does not disconnect V.

The Geometry of Divisors on Matroids

arrangements has led to fruitful interactions between algebraic geometry and matroid theory. A notable example is the development of the Hodge theory of matroids [AHK18], a breakthrough that resolved many long-standing conjectures in matroid theory. The central object in the Hodge theory of matroids is the Chow ring A (M) of a

University of California, Berkeley

1 Abstract The Generalized External Order, and Applications to Zonotopal Algebra by Bryan R. Gillespie Doctor of Philosophy in Mathematics University of California, Berkeley Profe

GRANT PROPOSAL TITLE PAGE Principal Investigator

The discrete geometry of polyhedra and lattices is connected to Algebraic Geometry. Toric varieties are algebraic varieties that come with a polyhe-dral dictionary from which one can read off algebraic invariants. Ideas from 2

CURRICULUM VITAE FOR HENRY K. SCHENCK

PI-NSA grant (Toric varieties, hyperplane arrangements, splines), $56,150, 2011-2013. 8. PI-UIUC Research Board (Approximation theory and geometry), $13,000 for a GRA 2012-2013.

INTERNATIONAL CONFERENCE ON TORIC TOPOLOGY

Toric structures on near-symplectic manifolds Right side: Takeshi KAJIWARA (Tohoku University) Toric geometry and tropical geometry 15:30{15:45 Cofiee 15:45{16:15 Left side: Catalin ZARA (Univ of Massachusetts at Boston) Hamiltonian GKM spaces and their moment graphs Right side: Hui LI (University of Luxembourg)

THE FACES OF TORIC ARRANGEMENTS

ing arrangements on the torus, which is called toric arrangement. Our research is conducted based on some of their work and we are also inspired a lot by Stanley s study in hyperplane arrangement. In our research, we did some analog versions of Stanley s theorem in toric arrangement, and

Max Kutler: Curriculum Vitae

Combinatorics and algebraic geometry. Particular areas of interest include tropical and non-archimedean geometry, toric and hypertoric varieties, hyperplane arrangements, matroids, and combinatorial Hodge theory. Research Publications 9.The motivic zeta functions of a matroid, with D. Jensen and J. Usatine.arXiv:1910.01291, J. London Math.

MARGARET A. READDY CURRICULUM ITAE

Toric arrangements 2010 Institute for Advanced Study, Geometry and Cell Complexes Seminar, Princeton, NJ Flag enumeration in geometry and algebra 2010 University of Pennsylvania CAGE (Combinatorics & Algebraic Geometry) Seminar 2010 University of Kentucky Colloquium The cd-index of balanced and Bruhat graphs

Likelihood Geometry - UniFI

favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes are written for the second author s lectures at the CIME-CIRM

A survey on arithmetic Tutte polynomials : motivations

hyperplane arrangements, but di erent toric arrangements! In other words, let X be a list of vectors with integer coordinates. The geometry of the corresponding toric arrangements depends on the linear algebra and on the arithmetics of X ; so we need a combinatorial structure keeping track of both.

TORIC PARTIAL ORDERS - www-users.math.umn.edu

examples of unimodular toric arrangements discussed by Novik, Postnikov and Sturmfels in [19, §§4-5]; see also Ehrenborg,Readdy and Slone [10]. Definition 1.1. A connected componentc of the complement RV /ZV −A tor(G) is called a toric chamber for G; denote by ChamA tor(G) the set of all toric chambers of A tor(G).

Fundamental groups and cohomology jumping loci

Fundamental groups and geometry Fundamental groups The fundamental group Definition (Poincaré 1904) Given a topological space X, and a basepoint x0 2X, let ˇ1(X;x0) = floops at x0g= This is a group, with multiplication = concatenation of loops, unit = constant loop, and inverse = reversal of loop.

Sage 9.3 Reference Manual: Combinatorial and Discrete Geometry

Sage 9.3 Reference Manual: Combinatorial and Discrete Geometry, Release 9.3 Sage includes classes for hyperplane arrangements, polyhedra, toric varieties (including polyhedral cones and fans),