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--- seminars:comb:start [2024/02/27 12:02]
zaslav [SPRING 2024]
+++ seminars:comb:start [2024/04/29 01:00] (current)
zaslav [SPRING 2024]
@@ Line 70: / Line 70: @@
 Location:  WH 100E
-A triangulation of an oriented matroid is a combinatorial analog to a geometric triangulation of the convex hull of a set of points in affine space. Even finding a good definition of oriented matroid triangulation is surprisingly tricky, and the most fundamental conjecture -- that such a triangulation should be a topological ball -- has been open for many years.
+A triangulation of an oriented matroid is a combinatorial analog to a geometric
+triangulation of the convex hull of a set of points in affine space. Even finding
+a good definition of oriented matroid triangulation is surprisingly tricky, and
+the most fundamental conjecture -- that such a triangulation should be a
+topological ball -- has been open for many years.
-This talk is a historical survey, as well as an appeal for a new generation to take up the quest.
+This talk is a historical survey, as well as an appeal for a new generation
+to take up the quest.
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@@ Line 82: / Line 87: @@
 <HTML><li></HTML>**Tuesday, 3/12**\\
 Speaker: Yichen Ma (Cornell) \\
-Title:: Invariants of partial orders and convex geometries via characters on Hopf monoids \\
+Title:: Invariants of Partial Orders and Convex Geometries via Characters on Hopf Monoids \\
 Time: 1:15-2:15\\
 Location:  WH 100E
@@ Line 100: / Line 105: @@
 We also describe the coefficients of the quasisymmetric invariants as
 enumerating faces on certain simplicial complexes. These include the
-barycentric subdivision of the CW-sphere of a convex geometry introduced by Billera, Hsiao and Provan.
+barycentric subdivision of the CW-sphere of a convex geometry introduced
+by Billera, Hsiao and Provan.
 <HTML></li></HTML>
 <HTML><li></HTML>**Tuesday, 3/19**\\
-Speaker: Michael Gottstein (Binghamton)\\
+Speaker: Thomas Zaslavsky (Binghamton)\\
-Title: TBA\\
+Title: Correlation Clustering: Signed Graphs, Algorithms, and a Best Case\\
 Time: 1:15-2:15\\
 Location:  WH 100E
+A signed graph has its edges labelled positive and negative; we regard an edge
+as agreement ($+$) and disagreement ($-$) between its endpoints.
+A clustering is a partition of the vertex set into subsets, called "clusters".
+Correlation clustering, introduced by Bansal et al., wants all edges within a cluster to represent agreement
+($+$) and all edges between clusters to represent disagreement ($-$), but that
+is rarely possible, so it seeks to minimize the number of "bad" edges: positive edges
+between clusters and negative edges within clusters; this
+minimum is the "clusterability index" $Q$ and its realization is an "optimal
+clustering".  Finding $Q$ or an optimal clustering is NP-hard, but there is a
+simple lower bound on $Q$ which is attained under certain conditions.
+The signed graphs that meet those conditions, and their optimal clusterings,
+can be described precisely.
+This work is joint with Leila Parsaei-Majd and Michael Gottstein.
+The talk can be regarded as an introduction to signed graphs.
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 <HTML><li></HTML>**Tuesday, 3/26**\\
 Speaker: Peter Maceli (Ithaca)\\
-Title: \\
+Title: Structure of Self-Complementary Graphs \\
 Time: 1:15-2:15\\
 Location:  WH 100E
+A graph is called self-complementary if it and its complement are isomorphic.
+The class of self-complementary graphs is structurally and algorithmically very rich,
+yet little is known about decomposing or explicitly constructing such graphs.
+I will discuss a structural conjecture of Trotignon, as well as a number of
+general techniques for constructing self-complementary graphs.
 <HTML></li></HTML>
 <HTML><li></HTML>**Tuesday, 4/2**\\
-Speaker: **Tentative**  Thomas Zaslavsky (Binghamton)\\
+There will be no seminar today as we prepare for the solar eclipse.  Remember not to look at the 97%-eclipsed sun without adequately dark glasses.
-Title: Correlation Clustering: Algorithms and Signed Graphs\\
-Time: 1:15-2:15\\
-Location:  WH 100E
 <HTML></li></HTML>
 <HTML><li></HTML>**Tuesday, 4/9**\\
-Speaker: Marwa Mosallam (Binghamton)\\
+Speaker: Quaid Iqbal (Binghamton)\\
-Title: Characteristic Sets of Matroids\\
+Title: Description of Distance-Regular Graphs with Fixed Parameters\\
 Time: 1:15-2:15\\
 Location:  WH 100E
+A graph $\Gamma$ is distance regular if, for any two vertices $v$ and $w$ at
+distance $d$, the number of vertices at distance $j$ from $v$ and distance $k$
+from $w$ depends only on $d, j$, and $k.$ Distance-regular graphs have
+very nice eigenvalue properties (e.g., they have $d+1$ distinct eigenvalues)
+and are a lively topic in spectral graph theory. Distance-regular graphs with
+diameter $2$, which are called strongly regular, have been important in the
+classification of finite groups. Given a graph $\Gamma$, the distance-$2$
+graph $\Gamma_2$ is the graph on the same vertices, in which vertices are
+adjacent if they have distance $2$. I consider the distance-regular graphs
+$\Gamma$ whose distance-$2$ graphs $\Gamma_2$ are strongly regular. If $\Gamma$
+is bipartite, then its distance-$2$ graph is not connected. So, I am interested
+in the class of non-bipartite distance-regular graphs. I explain that it can be
+described with a fixed parameter, that is by eigenvalue or by intersection number.
+First, I will show that the distance-$2$ graph of a non-bipartite distance-regular
+graph with diameter $D=3,4$ and eigenvalue $a_ {2}-c_ {3} $ is strongly regular,
+and then I will give several kinds of  descriptions of non-bipartite
+distance-regular graphs with diameter $D=3,4$ and eigenvalue $a_ {2}-c_ {3}$
+under various conditions, for example when the $\tilde{c} =p$ (prime)
+(where $\tilde{c}$ is the number of common neighbors between any two non-adjacent
+vertices).
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@@ Line 139: / Line 185: @@
 Speaker: Michael Gottstein (Binghamton)\\
 Title: Partitions and Gain Graphs\\
-Time: 1:15-2:15 (and another hour to be determined)\\
+Time and Location: 1:15-2:15 in WH 100E and 3:00-4:00 in WH 309\\
-Location:  WH 100E\\
+The Rhodes semilattice of a group is a fundamental tool used in the complexity theory
+of finite semigroups. I reinterpret the Rhodes semilattice into the language of
+gain graphs. This reinterpretation naturally suggests several lattice extensions
+of the Rhodes semilattice. One of these lattices can be seen as a vast generalization
+of finite groupoids. The objective of this defense is to demonstrate
+and support this point of view.
 This is Mr. Gottstein's Ph.D. thesis defense.  The examining committee consists of
@@ Line 154: / Line 206: @@
 for Infinite Graphs\\
 Time: 1:15-2:15\\
-Location:  WH 100E and Zoom\\
+Location:  WH 100E and Zoom https://binghamton.zoom.us/j/3475600721 \\
 Nash-Williams proved in 1960 that an edge connectivity of 2k is sufficient

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