\nAfter a short introdu ction into general theory of currents mod(p)\, I will give you glimpse on the previously known results and on our new bound on the Hausdorff dimensi on of the set. If time permits I will give a short outlook of what we woul d be the expected result.\n LOCATION:https://researchseminars.org/talk/OSGA/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Brendle (Columbia University) DTSTART;VALUE=DATE-TIME:20201027T180000Z DTEND;VALUE=DATE-TIME:20201027T190000Z DTSTAMP;VALUE=DATE-TIME:20221209T232324Z UID:OSGA/37 DESCRIPTION:Title: Th e isoperimetric inequality for minimal surfaces\nby Simon Brendle (Col umbia University) as part of Online Seminar "Geometric Analysis"\n\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/OSGA/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Campbell (University of Hradec Kralove) DTSTART;VALUE=DATE-TIME:20201020T170000Z DTEND;VALUE=DATE-TIME:20201020T180000Z DTSTAMP;VALUE=DATE-TIME:20221209T232324Z UID:OSGA/38 DESCRIPTION:Title: Pa thological Sobolev homeomorphisms in GFT and NE\nby Daniel Campbell (U niversity of Hradec Kralove) as part of Online Seminar "Geometric Analysis "\n\n\nAbstract\nSobolev homeomorphisms are the natural choice for minimiz ation problems in non-linear elasticity. For the regularity of these probl ems it would be useful to be able to approximate these maps by smooth home omorphisms in their corresponding Sobolev space (the so-called Ball-Evans problem). We construct a pair of homeomorphisms for which is impossible si multaneously solving the Hajlasz problem. That is we construct a Sobolev h omeomorphism equalling identity on the boundary of a cube but with negativ e Jacobian almost everywhere.\n LOCATION:https://researchseminars.org/talk/OSGA/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Ursula Ludwig (University of Duisburg-Essen) DTSTART;VALUE=DATE-TIME:20201208T180000Z DTEND;VALUE=DATE-TIME:20201208T190000Z DTSTAMP;VALUE=DATE-TIME:20221209T232324Z UID:OSGA/39 DESCRIPTION:Title: An Extension of a Theorem by Cheeger and Müller to Spaces with Isolated Con ical Singularities\nby Ursula Ludwig (University of Duisburg-Essen) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nAn important c omparison theorem in global analysis is the comparison of analytic and top ological torsion for smooth compact manifolds equipped with a unitary flat vector bundle. It has been conjectured by Ray and Singer and has been ind ependently proved by Cheeger and Mu ̈ller in the 70ies. Bismut and Zhang combined the Witten deformation and local index techniques to generalise t he result of Cheeger and Mu ̈ller to arbitrary flat vector bundles with a rbitrary Hermitian metrics. The aim of this talk is to present an extensio n of the Cheeger-Mu ̈ller theorem to spaces with isolated conical singula rities by generalising the proof of Bismut and Zhang to the singular setti ng.\n LOCATION:https://researchseminars.org/talk/OSGA/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Behnam Esmayli (Uni of Pittsburgh) DTSTART;VALUE=DATE-TIME:20201117T180000Z DTEND;VALUE=DATE-TIME:20201117T190000Z DTSTAMP;VALUE=DATE-TIME:20221209T232324Z UID:OSGA/40 DESCRIPTION:Title: Co -area formula for maps into metric spaces\nby Behnam Esmayli (Uni of P ittsburgh) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nC o-area formula for maps between Euclidean spaces contains\, as its very sp ecial cases\, both Fubini's theorem and integration in polar coordinates f ormula. In 2009\, L. Reichel proved the coarea formula for maps from Eucli dean spaces to general metric spaces. I will discuss a new proof of the la tter by the way of an implicit function theorem for such maps. An importan t tool is an improved version of the coarea inequality (a.k.a Eilenberg in equality) that was the subject of a recent joint work with Piotr Hajlasz. Our proof of the coarea formula does not use the Euclidean version of it a nd can thus be viewed as a new (and arguably more geometric) proof in that case as well.\n LOCATION:https://researchseminars.org/talk/OSGA/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Hermann Karcher (University of Bonn) DTSTART;VALUE=DATE-TIME:20201215T180000Z DTEND;VALUE=DATE-TIME:20201215T190000Z DTSTAMP;VALUE=DATE-TIME:20221209T232324Z UID:OSGA/41 DESCRIPTION:Title: Nu merical experiments with closed constant curvature space curves\nby He rmann Karcher (University of Bonn) as part of Online Seminar "Geometric An alysis"\n\n\nAbstract\nThe discovery story will be told with pictures illu strating all steps\, including the

($\\pi p/q$)\,\nthen the curves are again forced by their symmetries to close up. Therefore\non e can hope to get examples by solving a 2-parameter problem.\n\nThis is ma de simple by an