The study of totally geodesic submanifolds has played an important role in our understanding of hyperbolic surfaces and 3-manifolds. In this talk we will discuss some of these developments as well as analogous questions in higher dimensions.
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All day |
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4:00pm |
04/05/2022 - 4:15pm The study of totally geodesic submanifolds has played an important role in our understanding of hyperbolic surfaces and 3-manifolds. In this talk we will discuss some of these developments as well as analogous questions in higher dimensions. Location:
https://yale.zoom.us/j/94256436597
04/05/2022 - 4:30pm In this talk, we revisit the famous Zagier formula for multiple zeta values (MZV's) and its odd variant for multiple $t$-values which is due to Murakami. $$\displaystyle H(a, b)=\zeta(\underbrace{2, 2, \ldots, 2}_{\text{$a$}}, 3, \underbrace{2, 2, \ldots, 2}_{\text{$b$}}).$$ which can be expressed as a $\mathbb{Q}$-linear combination of products $\pi^{2m}\zeta(2n+1)$ with $m+n=a+b+1$. This formula for $H(a, b)$ played a crucial role $$\displaystyle T(a, b)=t(\underbrace{2, 2, \ldots, 2}_{\text{$a$}}, 3, \underbrace{2, 2, \ldots, 2}_{\text{$b$}}).$$ We show the parallel of the two formulas for $H(a, b)$ and $T(a, b)$ and derive elementary proofs by relating both of them to a surprising cotangent integral. Also, if time will allow, Location: |
Links
[1] https://math.yale.edu/calendar/grid/day/2022-04-04?field_calendar_tags_tid_selective=%5Btid%5D
[2] https://math.yale.edu/calendar/grid/day/2022-04-06?field_calendar_tags_tid_selective=%5Btid%5D
[3] https://math.yale.edu/event/hyperbolic-manifolds-and-their-totally-geodesic-submanifolds
[4] https://math.yale.edu/event/zagiers-formula-multiple-zeta-values-and-its-odd-variant-revisited
[5] https://math.yale.edu/print/list/calendar/grid/day/2022-04-05
[6] webcal://math.yale.edu/calendar/export.ics