# Combinatorics, Algebra and Geometry Seminar (CAGS)

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## Combinatorics, Algebra and Geometry Seminar (CAGS)

I am planning to have all our CAGS talks conducted a hybrid fashion; both in person and on Zoom. Some CAGS talks, international talks for example, will only be virtual on Zoom. All talks will be given 12:30 -- 1:30 PM on Fridays in our seminar room **Exploratory Hall, room 4106.** unless otherwise stated. The room is equipped with white boards, and a projector. -- If you like to participate please send me, your devoted CAGS Chair, an email and I will try my best to schedule your talk. If you prefer to give a Zoom talk then I will send you a Zoom invitation.

**CAGS Chair**: Geir Agnarsson

The **CAGS** is intended as an informal venue, where faculty members, graduate students, visitors from near and far can come and give informal talks on their research, interesting new topics, open problems or just share their thoughts/ideas on anything interesting relating to combinatorics, algebra and discrete geometry. Needless to say, all are welcome to attend, and those who want to give a talk, should email me Geir ("gagnarss followed by the at sign gmu dot edu") the title and a short abstract. The talks should be no longer than 50 minutes long; leaving a few minutes for questions, comments and further discussions afterwards.

For other seminars and regular meetings, check our departmental Seminars & Colloquiums

## Spring 2024

**February 9**

Helly-Type Theorems on Support Lines for Families of Congruent Disks in the Plane

Tyler Russ, George Mason University

**February 16**

Hamiltonicity and related properties in K_{r+1}-free graphs

Aleyah Dawkins, George Mason University

**March 15**

Compatible transfer systems for *C _{p}^{r}_{q}^{s}*

Valentina Zapata Castro, University of Virginia

**March 22**

On locally finite ordered rooted trees and their rooted subtrees

Aleyah Dawkins, George Mason University

**April 5**

Research directions on Hopf algebras

Van Nguyen

**April 19**

Mark Burge

## Past Seminars

### Fall 2023

**September 22**

Recent Developments s in the Fundamental Theorem of Algebra

Mohsen Aliabadi, University of California San Diego

**September 29 (virtual, on Zoom)**

On the Partition Regularity of ax + by = cw^{m}z^{n}

Sohail Farhangi, The University of Adam Mickiewicz, Poznan, Poland

**October 13**

When is the group of units as additively closed as

possible?

Neil Epstein, George Mason University

**October 20**

How to show that a ring has uncountable krull

dimension

Jack J Garzella, University of California San Diego

**October 27**

Combinatorial Aspects of the Alternating Sign Matrix

Elizabeth A. Dinkelman, George Mason University

**December 1 at 11:00am (virtual, on zoom)**

Real-time Formalization of Mathematics

Kevin Buzzard, Imperial College, London, United Kingdom

### Spring 2023

### Spring 2023

**February 3 - In person and zoom**

Neil Epstein, GMU

**March 3 - In person and zoom**

Helly-type theorems on support lines for convex bodies in the plane

Valeriu Soltan, GMU

**March 24 - Zoom**

Generalized Turán problems and a new localized approach

Rachel Kirsch, GMU

**April 7 - Zoom**

Reem Mahmoud, Virginia Commonwealth University,

**April 14 - In person and zoom**

Scott Carson, GMU

**April 28 - In person and zoom**

Multiplier ideals and klt singularities via (derived) splittings

Peter Morton McDonald, University of Utah

**May 3 - In person and zoom - 11am-12pm - Note! Unusual day and time**

Perfectoid signature and an application to étale fundamental groups

Karl Schwede, University of Utah

### Fall 2022

**October 28 - In-person and Zoom**

Global perinormality in a generalization of a D +M construction and graded perinormality

Hannah Klawa, GMU

**November 4 - In-person and Zoom**

Infinitude Results for Prime Polynomials

Brian L. Johnson, Northern Virginia Community College

**November 11 - In-person and Zoom - The talk is postponed until further notice.**

Perfectoid signature and an application to étale fundamental groups -

Karl Schwede, The University of Utah

**November 16 - Zoom ***(NB! Unusual time: Wednesday 12:30 -- 1:30 PM EST)*

Parity property of hexagonal sliding puzzles

Érika Roldán, The Max Planck Institute

**November 18 - Zoom**

Magnús Már Halldórsson, Reykjavık University, Iceland

**December 2 - In-person and Zoom - ***(NB! Unusual time: 2:30 -- 3:30 PM EST)*

Distractions and Generic Initial Ideals

Anna-Rose Wolff, Mary Baldwin University

### Spring 2022

**February 24 **(virtual)

Canonical forms of neural ideals

Rebecca R.G., George Mason University

**March 11 **(in person)

Boundedly Polyhedral Sets and F-Simplices

Valeriu Soltan, George Mason University

**March 25 **(in person and virtual)

Promotion, rotation, and a web basis of invariant polynomials from noncrossing partitions

Jessica Striker, North Dakota State University

**April 1 **(in person and virtual)

Arithmetic Dynamics on Character varieties

Cigole Thomas, George Mason University

**April 8 **(in person and virtual)

Richard H. Hammack

**April 22 **(virtual) - **Postponed until Fall 2022**

Parity Property of Hexagonal Sliding Puzzles

Érika Roldán, Technische Universitat Munchen

### Fall 2021

- October 8 (virtual)~ Groups, lattices, and closure operators

Arturo Magidin - October 15 (virtual)~ Permutation statistics and moment sequences

Einar Steingrímsson - October 29 (virtual)~ Higher dimensional origami constructions

Adriana Salerno - November 5 (virtual)~ Universal Partial Cycles

Rachel Kirsch - November 12~ Hurwitz action in complex reflection groups

Jiayuan Wang - December 3 (virtual)~ Deep neural networks and DNA variant effect predictions in humans

Ágúst Egilsson

### Spring 2021

- February 26~ Ideals of skew-symmetric matrix Schubert varieties

Brendan Pawlowski - March 12~ Whitney duals and Whitney twins: a plausible approach to questions related to Whitney numbers

Rafael S. González Di León - March 19~ Sum-product and convexity

Brandon Hanson - April 9~ Probabilistic generalizations of the Robinson– Schensted correspondence

Gabriel Frieden - April 16~ Steiner configurations ideals: containment and colorability

Abu Chackalamannil Thomas - April 23~ Data Science – Requirements and Applications

Colton Magnant

### Fall 2020

- September 18~ Dedekind, Prüfer, Krull, and factorial rings with or without zerodivisors

Jesse Elliot - September 25~ The Free Cone and its relation to matroid invariants

Kevin Long - October 2~ Independent sets, Lovasz’ theta, and linear programming

Craig E. Larson - October 16~ From Efron's coins to alternation acyclic tournaments

Gabor Hetyei - October 23~ Minimal free resolutions of fiber products

Hugh R. Geller - October 30~ Separating hyperplanes of convex sets

Valeriu Soltan

### Spring 2020

- January 31~ ECH capacities, Ehrhart theory, and toric varieties

Ben Wormleighton - February 7~ Connected sums of Gorenstein Artin rings

Ela Celikbas - February 21~ Tiling, Terry Tao, Group Characters, and Fugledes Conjecture

Sam Ferguson - March 20~ TBA Postponed until further notice!

Jack Love - March 27~ TBA Postponed until further notice!

Jesse Elliott - April 24~ Independent sets, Lovasz’ theta, and linear programming Postponed until further notice!

Craig E. Larson - May 1~ TBA Postponed until further notice!

Kevin Long

### Fall 2019

- September 13~ A few problems on matrix rings

Geir Agnarsson - September 20~ Magic type labelings of cycle products

Dalibor Froncek - September 27~ Generalized Rings

Carl Weisman - October 18~ Involutions and pseudo-involutions in the Riordan group

Alexander Burstein - November 1~ The ring of differential operators in a generalized Stanley-Reisner ring

Janet Vassilev - November 15~ M-decomposable convex sets

Valeriu Soltan - November 22~ Trace modules over commutative rings

Haydee Lindo - December 6~ The dynamics of Boolean networks

Reinhard Laubenbacher

### Spring 2019

- February 1~ Vertex colorings of acyclic digraphs, efficiencies and discrepancies

Geir Agnarsson - March 1~ Lech’s inequality and the Stuckrad-Vogel conjecture

Patricia Klein - March 29~ Counting factorizations in complex reflection groups

Joel Brewster Lewis - April 5~ On the number of discrete chains

Eyvindur Ari Pállson - April 12~ Minimal generating sets for coordinate rings of representations

Sean Lawton - April 19~ Circular coloring of planar graphs

Dan Cranston - May 3~ No CAGS talk (MEGL poster session, hallway right outside EXPL 4106)

GMU mathematics students.

### Fall 2018

- September 7~ A proof of the strict monotone 5-step conjecture

Walter Morris - September 14~ Pseudoalgebras

Carl Weisman - October 5~ Moreau-Type Characterizations of Polar Cones

Valeriu Soltan - October 19~ Positivity in the S1-equivariant cohomology of type A Peterson varieties

Brent Gorbutt - October 23~Tuesday\ 11 am -- 12 noon, ROOM 3301 EXPL. HALL. Polymatroids and excluded minors

Carolyn Chun - November 2~ Nearly Platonic graphs

Dalibor Froncek - November 9~ Helly-type results on support lines for disjoint families of unit disks

Valeriu Soltan - November 30~ The role of big Cohen-Macaulay modules and algebras in commutative algebra

Rebecca R.G.

### Spring 2018

- February 2~ Interval posets, parity representations, binary partitions, and antiprisms (Part I: 12:30 -- 1:00 pm)

Jim Lawrence - February 9~ Interval posets, parity representations, binary partitions, and antiprisms (Part II)

Jim Lawrence - February 23~ Colored subgraphs whose forbiddance implies monochromatic connectivity

Colton Magnant - March 2~ When does the content map on polynomials act like a homomorphism, and how broadly does the answer apply? (Postponed until March 9)

Neil Epstein - March 30~ Hamiltonian cycles in critical graphs with large maximum degree

Yue Zhao - April 6~ Routing numbers of some graphs

Gexin Yu - April 13~ The Set-Maxima problem

Indranil Banerjee - April 27~ Diffuse Interfaces and Topology: A Phase-Field Model for Willmore’s Energy (Special Applied Math and CAGS Joint Seminar)

Stephan Wojtowytsch - May 4~ Applications of ordinary voltage graph theory and intersection theory to graph embeddability, (and some notes about topological data analysis) (NB! 11:30 am, due to Math Dept luncheon)

Steven Schluchter

### Fall 2017

- September 8~ Sequential Importance Sampling Algorithms for Estimating Tree Size

Alathea Jensen - September 15~ Extremal finite subgraphs of the grid graph

Geir Agnarsson. - October 6~ Permutation Routing Via Matchings

Indranil Banerjee. - October 20~ SIAM Faculty Seminar
- October 27~ Separation and polarity properties of convex cones

Valeriu Soltan. - November 3~ Algebraic and combinatorial interpretations of tight closure theory on Stanley-Reisner rings

Thomas Ales. - November 10~ Unbalanced Wilf-equivalence

Alexander Burstein. - December 1~ TBA postponed!

Jacob Farinholt - December 8~ Symbolic powers and differential operators

Eloísa Grifo

### Spring 2017

- February 10~ Generalized depth in the perfect closure

George E. Whelan - February 24~ Acyclic digraphs giving rise to complete intersections

Walter Morris - March 3~ How well-behaved is your ring map? The Ohm-Rush content function reconsidered

Neil Epstein - March 24~ Distance magic and group distance magic graphs

Dalibor Froncek - April 21~ Edge-coloring of graphs and multigraphs

Dan Cranston - April 28~ Conjugation of Transitive Permutation Pairs and Dessins d'Enfants

Sean J. Rostami - May 5~ Hessenberg varieties and the Shareshian-Wachs conjecture

Patrick Brosnan

### Fall 2016

- September 9~ Doubly weighted rooted trees and computer security systems

Geir Agnarsson - October 7~ Self-polar polytopes

Alathea Jensen - October 14~ A great tool from the polynomial method toolkit: the Alon-Füredi Theorem

John R. Schmitt - October 27~ NB! Thursday at 12 noon Decompositions of complete bipartite graphs into generalized prisms

Dalibor Froncek - October 28~ A new perspective on the G-Invariant of a matroid

Joseph E. Bonin - November 4~ Khovanskii bases, Newton-Okounkov polytopes, and tropical geometry of projective varieties

Chris Manon - November 18~ Minimal ring extensions

Jay Shapiro

### Spring 2016

- February 12~ Max-weight rooted-subtree problem and computer security

Geir Agnarsson - March 4~ A directed Steinitz theorem for oriented matroid programming

Walter Morris - March 18~ Characteristic properties of ellipses

Valeriu Soltan - March 25~ The Diophantine Frobenius Problem: Past, Present and Future

Elie Alhajjar - April 1~ Even the Patriots can win Atlantic 10!

Dalibor Froncek - April 5~NB! Tuesday at 12:30! On the Maximum Genus of Planar Graphs

Lara Sherif - April 8~ Matrix rings and representations

Sam Mendelson - April 22~ Geometry of Peterson Varieties in Lie Type A

Brent Gorbutt - April 29~NB! At 12 noon! In pursuit of canonical structures on cellularly embedded graphs

Jason Suagee

### Fall 2015

- September 18~ Differential graded manifolds as a model for derived manifolds

David Carchedi - October 2~ On a special class of general permutahedra

Geir Agnarsson - October 16~ Negatively Self-Polar Polytopes

Alathea Jensen - October 30~ LP Alchemy for the Stability Number of a Graph

Craig Larson - November 6~ Prime congruences and Krull dimension for additively idempotent semirings

Kalina Mincheva - November 13~ On the Geometry of Quantum Weak Measurements

Jacob Farinholt - December 4~ Self-dual embeddings of K_{4m,4n} in orientable and nonorientable pseudosurfaces with the same Euler characteristic

Steven Schluchter

### Spring 2015

- February 13~ Various generating functions, a unifying approach

Geir Agnarsson - February 20~ The Dedekind-Mertens Theorem for power series and more generally arbitrary algebras over R

Jay Shapiro - February 27~ The Zariski topology on sets of semistar operations

Dario Spirito - March 6~ Algebraic measures of singularity

Javid Validashti - March 20~ Graph Theory Tools for Tournament Scheduling

Dalibor Froncek - March 27~ Mihalisin - Klee Theorem for Fans

Rachel Locke - April 3~ Digital Geometry: New Trends and Developments

Li Chen - April 10~ The Complementarity Polytope, Pauli operators, and the Clifford Group

Jacob Farinholt - April 17~ Prime labelings of generalized Petersen graphs

Kathryn Cokus, Ryan Ellingson, and Thomas Wilson (co Justin Z. Schroeder and Steven Schluchter) - April 24~ The Survival Complex

Anna-Rose Wolff - May 1~NB! at 12 noon Homological algebra of graphs

Arindam Banerjee

### Fall 2014

- August 29~ Parking functions & friends

Matthias Beck - September 5~ Applications of ordinary voltage graph theory to graph embeddability, part I

Steve Schluchter - September 19~ Base-Orderability in Matroids

Thomas Savitsky - October 17~ The Traveling Salesman Problem and P vs. NP: Some 1960s Theoretical Work at NIST On the Complexity of Mathematical Algorithms

Jack Edmonds - October 24~ Poincare-Bett Series of Monomial Rings

Gwyneth Whieldon - October 31~ Valuations on Convex Sets

Jim Lawrence - November 7~ Puzzles and (many flavors of) Schubert calculus

Allen Knutson - November 14~ Applications of ordinary voltage graph theory to graph embeddability, part II

Steve Schluchter - Decemver 5~ Some special matrix algebra presentations

Samuel Mendelson

### Spring 2014

- January 31~ Induced subgraphs of hypercubes

Geir Agnarsson - February 21~ Mutually Unbiased Bases

Jacob Farinholt - February 28~ Ring extensions involving amalgamated duplications

Tim Long - March 28~ Triangle inequalities in representation theory and algebraic geometry

Chris Manon - April 4~ Ring extensions invariant under group action: flat epimorphic extensions

Amy Schmidt - April 11~ Test Ideals of Non-principal Ideals

Karl Schwede - April 18~ Threshold Digraphs

James Shook - May 2~at 12 noon! Strong Krull primes and flat modules

Neil Epstein

### Fall 2013

- September 6~ Informal discussion on Gelfand-Tsetlin Polytopes (ongoing)

Rebecca Goldin and Chris Manon - September 13~ Informal discussion on Gelfand-Tsetlin Polytopes (ongoing)

Rebecca Goldin and Chris Manon - September 20~ Some naturally occurring matroids and matroid-like structures in commutative algebra

Neil Epstein - September 27~ A survey on graphs with a distinguishing partition

Justin Z. Schroeder - October 4~ Complete Intersection Affine Semigroup Rings Arising from Posets

Walter Morris - October 11~ Informal discussion on Gelfand-Tsetlin Polytopes (ongoing)

Rebecca Goldin and Chris Manon - October 18~ Informal discussion on Gelfand-Tsetlin Polytopes (ongoing)

Rebecca Goldin and Chris Manon - October 25~ Ordinary voltage graphs, pseudosurfaces, and derived graph embeddings with applications to graph embeddability

Steven Schluchter - November 8~ Hom polytopes between regular polytopes

Jack Love - November 22~at 11:30am The geometry of the quotient stack arising from a stacky fan

David Johannsen

### Spring 2013

- February 1~ Schubert Calculus of Weighted Grassmannians

Tomoo Matsumura - February 8~ Zero-divisor graphs of nilpotent-free semigroups

Neil Epstein - February 15~ Coloring claw-free graphs with Δ-1 colors

Dan Cranston - March 1~ Zero-divisor graphs of nilpotent-free semigroups, part II

Neil Epstein - March 22~ "Graph" Saturation

Michael Jacobson - March 29~ Properties of the Copoint Graph of Convex Geometries

Jonathan Beagley - April 12~ Some basic properties of primary decomposition

Yongwei Yao - April 19~ Dimension and Height for Posets with Planar Cover Graphs

Noah Streib - April 26~ Approximating the Partition Function of the Ising Model

Amanda Streib - May 3~ Hyperbolic surfaces, circle maps and geometry of Teichmuller spaces

Dragomir Saric

### Fall 2012

- September 7~ Clique Number and Chromatic Number of Graphs defined by Convex Geometries

Walter Morris - September 14~ Algebra and geometry of archimedean integers in general number fields

Carl Weisman - September 28~ Going-down in monoid rings

Jay Shapiro - October 5~ Turning conformal field theory into combinatorics

Chris Manon - October 12~ A Happy Coloring Theorem

Jonathan Beagley - October 19~ Pebbling in Split Graphs

Glenn Hurlbert - November 2~ Multi-Sources Simultaneous Communication in the Wireless Mobility Model is NP-complete

Pattama Longani - November 16~ Some problems in ring theory

Geir Agnarsson

### Spring 2012

- February 3~ Schröder paths, partial horizontal strips, and symmetric functions

Sangwook Kim - March 2~ Davis matrics of sections and projections of polyhedral cones

Jim Lawrence - March 9~ On a Carathéodory theorem for Minkowski sum of polytopes

Geir Agnarsson - March 23~ Recent advances in biclique decompositions

Walter Morris - April 6~ On edge chromatic critical graphs

Yue Zhao - April 13~ Categorifications of the chromatic polynomial

Radmila Sazdanovic - April 20~ Carathéodory-type results for the sums and unions of convex sets

Valeriu Soltan NB! Postponed until further notice. - May 4~ Patterns in permutations

Alexander Burstein

### Fall 2011

- September 9~ Induced subgraphs of Z2 and related extremal graphs

Geir Agnarsson - September 16~ An abstract structure theorem for suborder lower ideals of series-parallel posets

Christian J. Altomare - September 23~ Hamilton Bond, Tutte Bond and Tutte Theorem

Xiaoyun Lu - October 7~ Global Weyl modules for twisted loop algebras

Prasad Senesi - October 21~ Tropical geometry of flag varieties and the space of phylogenetic trees

Chris Manon - October 28~ Art Galleries, Fortresses, and Prison Yards: Illumination and Color

T. S. Michael - November 4~ An Introduction to Simplicial Geometries

Cynthia S Merrick - November 11~ The Order Dimension of Convex Geometries

Jonathan Beagley - November 18~ Applying the stuff we like: blocking semiovals and cryptology

Keith Mellinger

### Spring 2011

- February 4~ The incidence algebra of a poset and enumerations

Geir Agnarsson - Febrary 18~ The type A Coxeter complex in algebraic combinatorics

Forest Fisher - Febrary 25~ A Projective approach to quantum error correcting codes

Jacob Farinholt - March 9, 12 noon -- 12:50 pm Unifying Laver's theorem and the Graph Minor Theorem via proof system minors

Christian Altomare Note! This talk is on a WEDNESDAY at noon! - March 11~ Convex quadrics

Valeriu Soltan - April 15~ A Projective approach to quantum error correcting codes, 2nd part

Jacob Farinholt - April 22~ Polytopes from graphs

Jim Lawrence - April 29~ Spies and revolutionaries

Dan Cranston

### Fall 2010

- September 10~ Oriented Matroids and N-step Vectors

Walter Morris - September 17~ Combinatorial identities for subspaces and finite sets

Geir Agnarsson - October 8~ Combinatorial Hopf algebras by way of groups

Forest Fisher, GWU - October 22~ Some Interesting Classes of Convex Polytopes

Jim Lawrence - November 12~ An Attempt to Turn Geometry into Decorated Graphs

Rebecca Goldin - November 19~ Homology of distributive systems: a historical perspective

Jozef Przytycki, GWU - December 3~ Points, Copoints, and Colorings

Jonathan Beagley - December 10~ New Results on Graph-Theoretic Independence

Craig Larson, VCU

### Spring 2010

- January 29~ The hitting time subgroup, Lukasiewicz paths, and Faber polynomials

Gi-Sang Cheon, SungKyunKwan University**S&T I room 242** - February 19~ Some graph labellings, complexities and connections to groups

Geir Agnarsson**S&T I room 206** - March 5~ Generalized rings: examples and applications

Carl Weisman**S&T I room 206** - March 19~ Workshop on Combinatorics, Enumeration, and Invariant Theory (WCEIT)
**S&T I room 242** - March 26~ Holes in a polytope defined by degree sequences

Walter Morris**S&T I room 206** - April 2~ On intersections and composites of minimal ring extensions

Jay Shapiro**S&T I room 206** - April 9~ Leavitt Path Algebras

Gene Abrams, University of Colorado at Colorado Springs**S&T I room 206** - April 23~ Ordered trees, the uplift principle and the Riordan group

Lou Shapiro, Howard University**S&T I room 206**

### Fall 2009

- September 18~ Survey of recent papers on the Hirsch conjecture

Walter Morris - September 25~ Making K-theory combinatorial

Rebecca Goldin - October 2~ Betti numbers of graphs

David Johannsen - October 16~ f- and h-vectors for complexes, polytopes and beyond

Geir Agnarsson - October 23~ How Five Regular Solids Turned into Seventy-five

Steve Morse - October 30~ Helly-Type Results on Common Supports of Convex Bodies

Valeriu Soltan - December 4~ Topology of real coordinate arrangements

Sangwook Kim

### Spring 2009

- January 30~ Mixed dominating matrices

Walter Morris - February 16 (Monday at 2:30 in S&T I, room 220)~ The Graham-Pollak Theorem and Alon-Saks-Seymour Conjecture

Reza Naserasr, Carleton University - February 27~ Embedding Quadratic Number Fields in Cyclotomic Fields

Bill Ellis - March 6~ Bruhat order and hyperplane arrangements

Sangwook Kim - March 20~ Thin Partially Ordered Sets

Mikhail Matveev - April 3~ The Geometry of Kissing: Soddy Circles, Apollonian Gaskets, and a Problem in Geometric Graph Theory

Jill Dunham - April 10~ On the flag polynomial of Minkowski sum of standard simplices

Geir Agnarsson

### Fall 2008

- September 12~ Szekeres and Peters' computer proof of the 17-point Erdos-Szekeres problem

Walter Morris - September 19~ On the structure of the Minkowski sum of standard simplices

Geir Agnarsson - September 26~ On the structure of the Minkowski sum of standard simplices, Part II

Geir Agnarsson - October 3~ The lattice of cyclic flats of a matroid

Joseph Bonin - October 17~ On Minkowski rings

Jim Lawrence - October 24~ On the openness of the contraction map to the fixed ring

Jay Shapiro - October 31~ The free splice of matroids

William Schmitt - November 7~ Rational Representations of Flowers

Jill Bigley Dunham - November 14,
**1:30 - 2:30**(NB! the time of the Applied and Computational Math Seminar)~ Random Threshold Graphs

Edward Scheinerman - November 21~ An Introduction to Lie Algebras and their Cohomology

Robert F. Allen

### Spring 2008

- January 30~ (no talk)
- February 6~ (no talk)
- February 13~ The importance of fixed points in group actions on symplectic manifolds

Rebecca Goldin - February 20~ On rational distances between points on a quadratic curve in the Euclidean plane

Steven D. Lepiere - February 27~ Some Combinatorial Types of Polytopes

Jim Lawrence - March 5~ Universal lying-over rings

Jay Shapiro - March 26~ Graph labeling, complexity and variants

Geir Agnarsson - April 2~ Graph labeling, complexity and variants (2nd part, but self-contained!)

Geir Agnarsson - Friday April 4, 11:30 - 12:30, Room 242 (NB! time and place)~ Horse racing, card games, theorems in matrix theory, and consequences

Chi-Kwong Li - April 9~ Simple vertices in a Minkowski sums of simplices

Walter Morris - April 16~ (no talk)
- April 23~ (no talk)
- April 30~ The Cantor Tree and things that are like it

Ronnie Levy

### Fall 2007

- Sept. 14~ Flag enumeration of matroid base poly\topes

Sangwook Kim - Sept. 21~ (no talk)
- Sept. 28~ Shellable complexes and topology of \diagonal arrangements

Sangwook Kim - Oct. 5~ Quadrilateral embedding of $G \times Q_s$\

Paul C. Kainen - Oct. 19~ Shellable complexes and topology of d\iagonal arrangements, part II

Sangwook Kim - Oct. 26~ Intordcutoin to Rnadom Garphs

Nate Shank - Nov. 9~ Graph theoretic proof of the Amitsur-Levits\ki theorem

Geir Agnarsson - Nov. 30~ We recommend the CDS/CCDS/Statistics Colloquium talk:

Social Networks via Random Dot Product Graphs

David Marchette

### Spring 2007

- Feb. 23~ Vertex coloring acyclic digraphs

Geir Agnarsson - Mar. 2~ Vertex coloring acyclic digraphs (Second Part)

Geir Agnarsson - Mar. 9~ (no talk)
- Mar. 16~ (Spring Break)
- Mar. 23~ An introduction to PPAD search problems

Walter Morris - Mar. 30~ (no talk, faculty meeting at 3:30)
- Aprli 6~ (no talk)
- April 13~ A quasisymmetric function for matroids

Louis J. Billera

NB! This is the first of two talks by Billera. The second talk will be later the same day at our departmental Colloquium. - April 20~ Simple Arrangements of Pseudolines, and their Other Lives

Jim Lawrence - Aprli 27~ (no talk)
- May 4~ The Euler characteristic and Euler's formula for convex polytopes (with proofs)

Jim Lawrence

### Fall 2006

- Sept. 15~ On Coin Graphs and Other Contact Graphs

Geir Agnarsson - Sept. 22~ Collineations and affine transformations in Euclidean space

Valeriu Soltan - Oct. 13~ Minkowski sums of simplices

Walter Morris - Oct. 20~ An algorithmic game related to Schubert calculus

Rebecca Goldin - Oct. 27~ Limits to Parallel Computation: P-Completeness Theory

Ray Greenlaw, Armstrong Atlantic State University and Fulbright Scholar at Chiang Mai University - Tuesday, Oct. 31, 12:15-1:05~ Physical Supersymmetry for Mathematicians

Greg Landweber, University of Oregon - Nov. 17~ Good Hidden P-matrix Sandwiches

Walter Morris

### Spring 2006

- Feb. 10~ Sunflowers, Kneser Graphs and Intersecting Families

Geoff McKenna, George Washington University - Feb. 17~ No talk. We recommend the department

colloquium at 3:30. - Feb. 24~ On the empty hexagon theorem

Walter Morris - Mar. 3~ Gale transforms

Jim Lawrence - Mar. 10~ More Gale Transforms: K_5 in R^3 (or S^3)

Jim Lawrence - Mar. 24~ No seminar. The Math Club is arranging a talk at 1:15, on the Mathematics of Juggling, by Allen Knutson, UCSD.
- Mar. 31~ The transfer of Krull dimension in fixed rings

Jay Shapiro - April 7~ Invariants of n-tuples of points on the Riemann sphere under linear fractional transformations

Ben Howard, UMCP - April 14~ On finite groups

Edith Adan-Bante, U. of Southern Mississippi Gulf Coast - May 4~ 3PM The plus, minus game

Klaus Fischer

### Fall 2005

- Sept. 8 ~ Graphical condensation and its connection to plane partitions and MacMahon's formula

Eric Kuo - Sept. 15 ~ A classification of the minimal ring extensions of an integral domain

Jay Shapiro - Sept. 22 ~ Combinatorics of Viterbi Sequences

Eric Kuo - Sept. 29 ~ The simple stochastic game

Walter Morris - Oct. 6 ~ Extension of vertex maps to graph homomorphisms

Geir Agnarsson - Oct. 13 ~ Extension of vertex maps to graph homomorphisms, part II

Geir Agnarsson - Oct. 20 ~ No talk
- Oct. 27 ~ Discrete polymatroids

Walter Morris - Nov. 3 ~ No talkNov. 10 ~ No talk
- Nov. 17 ~ Case Studies in Shape and Trajectory Optimization: Catenary Problem

Igor Griva - Dec. 1 ~ TBA

Jim Lawrence

### Spring 2005

- Feb. 18 ~ Isothetic Parallelotopes and the Binary Intersection Property

Valeriu Soltan - Mar. 4 ~ Cluttered orderings for the complete bipartite graph and the complete tripartite graph

Tomoko Adachi, Toho University, Japan - Mar. 11 ~ Positive bases in Euclidean space

Valeriu Soltan - Mar. 25 ~ On multipartite posets

Geir Agnarsson On multipartite posets - Apr. 1 ~ Algebra and graph reconstruction

Geoff McKenna, George Washington University Apr. 8 ~ NO TALK - we recommend the Math colloquium - Apr. 22 ~ Good hidden P-matrix sandwiches

Makoto Namiki, Toho University and George Mason University - Apr. 29 ~ Good hidden P-matrix sandwiches, part II

Makoto Namiki, Toho University and George Mason University