BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//UM//UM*Events//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:America/Detroit
TZURL:http://tzurl.org/zoneinfo/America/Detroit
X-LIC-LOCATION:America/Detroit
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
DTSTART:20070311T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:EST
DTSTART:20071104T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20260119T121312
DTSTART;TZID=America/Detroit:20260126T160000
DTEND;TZID=America/Detroit:20260126T170000
SUMMARY:Workshop / Seminar:GLNT: Ring of Modular forms on certain unitary Shimura Varieties
DESCRIPTION:The modular forms on the quotient $\mathrm{SL}_2(\mathbb{Z})\backslash \mathcal{H}$ can be viewed as $\mathrm{SL}_2(\mathbb{Z})$-invariant holomorphic differentials on $\mathcal{H}$. Interpreting $\mathrm{SL}_2(\mathbb{Z})\backslash \mathcal{H}$ as the moduli space of elliptic curves\, these forms can equivalently be described as global sections of the Hodge line bundle. A natural question is whether this perspective extends beyond $\mathrm{SL}_2(\mathbb{Z})$.\n\nIn this talk\, I will introduce modular forms on certain Shimura varieties and illustrate the definitions through a sequence of examples: Hilbert modular surfaces\, unitary Shimura curves\, and finally a unitary Shimura surface arising from a special family of cyclic covers of $\mathbb{P}^1$. I will explain how the geometry of this family makes the Hodge line bundle computable\, and how level structure on the Shimura variety can be interpreted concretely in this setting.
UID:143314-21892894@events.umich.edu
URL:https://events.umich.edu/event/143314
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260120T231803
DTSTART;TZID=America/Detroit:20260126T160000
DTEND;TZID=America/Detroit:20260126T170000
SUMMARY:Livestream / Virtual:Painlevé Universality class for the maximal amplitude solution of the Focusing Nonlinear Schrödinger Equation with randomness
DESCRIPTION:In this work\, we establish universality results for the $N$-soliton solution of the focusing NLS equation at maximal amplitude. Specifically\, we choose the associated normalization constants so that the solution achieves its maximal peak\, which\, in the large-$N$ limit\, satisfies a Painlevé-type equation independently of the distribution of the (random) discrete eigenvalues. We identify two distinct universality classes\, determined by the structure of the discrete eigenvalues: the \textit{Painlevé--III} and \textit{Painlevé--V} rogue-wave solutions. In the Painlevé--III case\, the eigenvalues take the form $\lambda_j = v_j + i \mu_j$\, while for Painlevé--V they satisfy $\lambda_j = -\zeta \\, j + v_j + i \mu_j$\, with $0 < \zeta < 1$. In both cases\, $v_j$ and $\mu_j$ are sub-exponential random variables. Universality can then be summarized as follows: regardless of the specific realizations of the amplitudes and velocities\, provided they are sub-exponential random variables and the normalization constants are chosen to maximize the \(N\)-soliton solution\, the resulting maximal peak always corresponds to either a Painlevé--III or Painlevé--V rogue-wave profile in the large-$N$ limit.
UID:142833-21891725@events.umich.edu
URL:https://events.umich.edu/event/142833
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics,Seminar,Virtual
LOCATION:Off Campus Location
CONTACT:
END:VEVENT
END:VCALENDAR