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Seminar information archive
Seminar information archive ～06/28｜Today's seminar 06/29 | Future seminars 06/30～
thesis presentations
14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)
thesis presentations
9:15-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
10:45-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
9:15-10:30 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
10:45-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
12:45-14:00 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)
2019/01/31
thesis presentations
12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)
thesis presentations
14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)
thesis presentations
15:45-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
thesis presentations
17:15-18:30 Room #118 (Graduate School of Math. Sci. Bldg.)
thesis presentations
12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
15:45-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
17:15-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
thesis presentations
9:15-10:30 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
10:45-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
15:45-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
thesis presentations
17:15-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
2019/01/30
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
2019/01/29
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Kentaro Mitsui (Kobe)
Logarithmic good reduction and the index (TBA)
Kentaro Mitsui (Kobe)
Logarithmic good reduction and the index (TBA)
[ Abstract ]
A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.
A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Salvatore Stuvard (The University of Texas at Austin)
The regularity of area minimizing currents modulo $p$ (English)
Salvatore Stuvard (The University of Texas at Austin)
The regularity of area minimizing currents modulo $p$ (English)
[ Abstract ]
The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.
It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.
The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.
It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.
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