@article{KhalilSchulze2019, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Calculus on a Manifold with Edge and Boundary}, series = {Complex analysis and operator theory}, volume = {13}, journal = {Complex analysis and operator theory}, number = {6}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-018-0800-y}, pages = {2627 -- 2670}, year = {2019}, abstract = {We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel's algebra (Acta Math 126:11-51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.}, language = {en} } @article{KhalilSchulze2017, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Boundary problems on a manifold with edge}, series = {Asian-European Journal of Mathematics}, volume = {10}, journal = {Asian-European Journal of Mathematics}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557117500875}, pages = {43}, year = {2017}, abstract = {We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel's theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.}, language = {en} } @phdthesis{Khalil2018, author = {Khalil, Sara}, title = {Boundary Value Problems on Manifolds with Singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-419018}, school = {Universit{\"a}t Potsdam}, pages = {10, 160}, year = {2018}, abstract = {In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel's calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions.}, language = {en} } @inproceedings{JacqminOezdemirFellKurbanetal.2021, author = {Jacqmin, Julien and {\"O}zdemir, Paker Doğu and Fell Kurban, Caroline and Tun{\c{c}} Pekkan, Zelha and Koskinen, Johanna and Suonp{\"a}{\"a}, Maija and Seng, Cheyvuth and Carlon, May Kristine Jonson and Gayed, John Maurice and Cross, Jeffrey S. and Langseth, Inger and Jacobsen, Dan Yngve and Haugsbakken, Halvdan and Bethge, Joseph and Serth, Sebastian and Staubitz, Thomas and Wuttke, Tobias and Nordemann, Oliver and Das, Partha-Pratim and Meinel, Christoph and Ponce, Eva and Srinath, Sindhu and Allegue, Laura and Perach, Shai and Alexandron, Giora and Corti, Paola and Baudo, Valeria and Turr{\´o}, Carlos and Moura Santos, Ana and Nilsson, Charlotta and Maldonado-Mahauad, Jorge and Valdiviezo, Javier and Carvallo, Juan Pablo and Samaniego-Erazo, Nicolay and Poce, Antonella and Re, Maria Rosaria and Valente, Mara and Karp Gershon, Sa'ar and Ruip{\´e}rez-Valiente, Jos{\´e} A. and Despujol, Ignacio and Busquets, Jaime and Kerr, John and Lorenz, Anja and Sch{\"o}n, Sandra and Ebner, Martin and Wittke, Andreas and Beirne, Elaine and Nic Giolla Mhich{\´i}l, Mair{\´e}ad and Brown, Mark and Mac Lochlainn, Conch{\´u}r and Topali, Paraskevi and Chounta, Irene-Angelica and Ortega-Arranz, Alejandro and Villagr{\´a}-Sobrino, Sara L. and Mart{\´i}nez-Mon{\´e}s, Alejandra and Blackwell, Virginia Katherine and Wiltrout, Mary Ellen and Rami Gaddem, Mohamed and Hern{\´a}ndez Reyes, C{\´e}sar Augusto and Nagahama, Toru and Buchem, Ilona and Okatan, Ebru and Khalil, Mohammad and Casiraghi, Daniela and Sancassani, Susanna and Brambilla, Federica and Mihaescu, Vlad and Andone, Diana and Vasiu, Radu and Şahin, Muhittin and Egloffstein, Marc and Bothe, Max and Rohloff, Tobias and Schenk, Nathanael and Schwerer, Florian and Ifenthaler, Dirk and Hense, Julia and Bernd, Mike}, title = {EMOOCs 2021}, editor = {Meinel, Christoph and Staubitz, Thomas and Schweiger, Stefanie and Friedl, Christian and Kiers, Janine and Ebner, Martin and Lorenz, Anja and Ubachs, George and Mongenet, Catherine and Ruip{\´e}rez-Valiente, Jos{\´e} A. and Cortes Mendez, Manoel}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-512-5}, doi = {10.25932/publishup-51030}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-510300}, pages = {vii, 295}, year = {2021}, abstract = {From June 22 to June 24, 2021, Hasso Plattner Institute, Potsdam, hosted the seventh European MOOC Stakeholder Summit (EMOOCs 2021) together with the eighth ACM Learning@Scale Conference. Due to the COVID-19 situation, the conference was held fully online. The boost in digital education worldwide as a result of the pandemic was also one of the main topics of this year's EMOOCs. All institutions of learning have been forced to transform and redesign their educational methods, moving from traditional models to hybrid or completely online models at scale. The learnings, derived from practical experience and research, have been explored in EMOOCs 2021 in six tracks and additional workshops, covering various aspects of this field. In this publication, we present papers from the conference's Experience Track, the Policy Track, the Business Track, the International Track, and the Workshops.}, language = {en} }