Faculty/Graduate Speaker Session

A look into the Hecke Algebra and the traces that act on it. When these traces act on certain elements of the Hecke Algebra, their output can be interpreted in terms of Young Tableaux in creative ways.
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This session shares initial research findings when STEM faculty engage in exemplar efforts towards continuous improvement in pedagogy. Undergraduate computer science and mathematics students participated in a student focus group, led by an educational researcher outside STEM, over their first 2 years in college. Focus group meetings engaged in robust discussion about successes and challenges as students transitioned to college and their chosen major. The educational researcher recorded, transcribed, and anonymized the data so that STEM faculty on the research team could then engage with the data and reflect on their classroom and student mentoring pedagogies. The presentation will provide example shifts in thinking about first year and intro-level courses, and with reflections on how STEM faculty have integrated these ideas into current practice. As a birds of a feather session, focus group data prompts will be shared with participants for roundtable discussions and collaborative discussion on best practices in STEM pedagogy and undergraduate mentoring.
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In 1972, Chvátal and Erdös proved the classical result that any graph whose independence number is at most its vertex-connectivity is Hamiltonian. This is best possible in the sense that if a graph has independence number more than its vertex-connectivity, it is no longer guaranteed to be Hamiltonian. We say a graph is nearly Chvátal-Erdös (or NCE) if its independence number is exactly one more than its vertex-connectivity. In this talk, we will discuss some properties of these graphs. Specifically, we provide the maximum size, i.e., number of edges, of an NCE graph along with the NCE graphs that achieve this maximum size. We will also summarize some additional results and present some ideas for further research.
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The Erdos--Ko--Rado (EKR) theorem, a foundational result in extremal finite set theory, states that any family of $k$-subsets of a finite set containing at least $2k$ elements that is intersecting, i.e. the family has the property that no two subsets in it are disjoint, can be no bigger than the family of all $k$-subsets containing a fixed element $x$. The latter family is trivially intersecting and is called a star centered at $x$. We discuss recent work on a graph-theoretic generalization of the theorem, partly inspired by a longstanding conjecture of Chvatal. We also consider a related problem of finding the optimal stars in this setting, a problem that highlights some of the underlying challenges posed by the conjecture.
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On a simple graph, a number of pebbles is placed at each vertex. A pebbling move involves removing two pebbles from one vertex and putting one extra pebble to a neighboring vertex. In this talk, we analyze a two-player version of this game, where the first player with no legal pebbling move loses. We also consider a few generalizations of this game.
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