seminars:comb:start
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seminars:comb:start [2024/03/24 20:06] zaslav [SPRING 2024] |
seminars:comb:start [2024/05/07 13:14] (current) laura |
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| <HTML><li></HTML>**Tuesday, 4/2**\\ | <HTML><li></HTML>**Tuesday, 4/2**\\ | ||
| - | Speaker: \\ | + | 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: \\ | + | |
| - | Time: 1:15-2:15\\ | + | |
| - | Location: WH 100E | + | |
| <HTML></li></HTML> | <HTML></li></HTML> | ||
| <HTML><li></HTML>**Tuesday, 4/9**\\ | <HTML><li></HTML>**Tuesday, 4/9**\\ | ||
| - | Speaker: \\ | + | Speaker: Quaid Iqbal (Binghamton)\\ |
| - | Title: \\ | + | Title: Description of Distance-Regular Graphs with Fixed Parameters\\ |
| Time: 1:15-2:15\\ | Time: 1:15-2:15\\ | ||
| Location: WH 100E | 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). | ||
| <HTML></li></HTML> | <HTML></li></HTML> | ||
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| Title: Partitions and Gain Graphs\\ | Title: Partitions and Gain Graphs\\ | ||
| Time and Location: 1:15-2:15 in WH 100E and 3:00-4:00 in WH 309\\ | Time and Location: 1:15-2:15 in WH 100E and 3:00-4:00 in WH 309\\ | ||
| + | |||
| + | 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 | This is Mr. Gottstein's Ph.D. thesis defense. The examining committee consists of | ||
| Line 181: | Line 206: | ||
| for Infinite Graphs\\ | for Infinite Graphs\\ | ||
| Time: 1:15-2:15\\ | 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 | Nash-Williams proved in 1960 that an edge connectivity of 2k is sufficient | ||
seminars/comb/start.1711325165.txt · Last modified: 2024/03/24 20:06 by zaslav