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Organizers:
Huitao Feng (Nankai, China)
Fei Han (NUS, Singapore)
Wilderich Tuschmann (KIT, Germany)
Kelin Xia (NTU, Singapore)
Scientific committee:
David Gu (Stony Brook, US)
Jürgen Jost (Max Planck Institutes, Germany)
Kefeng Liu (UCLA, US)
Guowei Wei (MSU, US)
Scope:
Data-driven
sciences are widely regarded as the fourth paradigm that can
fundamentally change sciences and pave the way for a new industrial
revolution. The great success of AlphaFold 2 in protein folding ushers
in a new era for machine learning models in natural sciences. However,
efficient representations and featurization are still one of the
central challenges for AI-based data analysis at present. Computational
and discrete geometry has achieved great success in data
characterization and modelling. In particular, geometric deep learning
has significantly advanced the capability of learning models for data
with complicated topological and geometric structures. The
combination of geometric methods with learning models has great
potential to fundamentally change the data sciences. As the field is
driven by a combination of deep mathematical methods and challenging
data, it is important to bring both sides together. This workshop will
focus on the recent progresses of geometric models in data
applications. The topics include but are not limited to:
- Discrete
exterior calculus and its application, discrete Laplace Operators,
discrete Optimal Transport, discrete mapping, discrete parametric
surface
- Geometric flow and applications (Ricci curvature flow, mean curvature flow, etc)
- Geometric modelling
- Discrete Ricci curvatures, Ollivier Ricci curvature, Forman Ricci curvature
- Conformal geometry
- Combinatorial Hodge theory, Hodge Laplacian, discrete Dirac operator
- Dimension
reduction (manifold learning, Isomap, Laplacian eigenmaps, diffusion
maps, UMAP, MAPPER, hyperbolic geometry, Poincaré embedding, etc)
- Geometric signal processing
- Geometric deep learning, graph neural network, simplex neural network
- Geometric analysis of deep learning, geometric GAN, explainable deep learning, geometric optimal transportation
- Index theory
- Gromov-Hausdorff distance
- Information geometry
- Metaverse: 3D vision, SLAM, digital geometry processing, digital manufacturing
The conference will be held in a hybrid form at Mathematical Science Research Center, Chongqing University of Technology, July 25-29, 2022. The zoom meeting details will be updated soon!
Confirmed Speakers:
Chandrajit Bajaj, University of Texas Austin, USA
Alexander Bobenko, TU Berlin, Germany
Shi-Bing Chen, University of Science and Technology of China, China
Mathieu Desbrun, California Institute of Technology, USA
Marzieh Eidi, Max Planck Institute for Mathematics, Germany
Michael Farber, Queen Mary University of London, UK
Mustafa Hajij, Santa Clara University, USA
Bobo Hua, Fudan, China
Parvaneh Joharinad, Max Planck Institute for Mathematics, Germany
Ye Ke, Chinese Academy of Sciences, China
Christian Kuehn, Technical University of Munich, Germany
Jiakun Liu, University of Wollongong, Australia
Shiping Liu, University of Science and Technology of China, China
Norbert Peyerimhoff, Durham University, UK
Konrad Polthier, Freie University of Berlin, Germany
Hong Van Le Prague, Czech Academy of Sciences, Czech Republic (Kyoto University, Japan)
Areejit Samal, The Institute of Mathematical Sciences, India
Emil Saucan,ORT Braude & Technion, Israel
Alexander Strang, The University of Chicago, USA
Junjie Wee, Nanyang Technological University, Singapore
Anna Wienhard, Heidelberg University, Germany
Jie Wu, BIMSA, China
Hao Xu, Zhejiang University, China
Dong Zhang, Max Planck Institute for Mathematics, Germany
Seminar Schedule (Titles and Abstracts & Recorded Videos!!)
The schedule is in China Standard Time (GMT+8)
| Beijing time | Berlin time (-6h) | London time (-7h) | New York time (-12h) | Sydney time (+2h) | | 2:00 PM | 8:00 AM | 7:00 AM | 2:00 AM | 4:00 PM | | 8:00 PM | 2:00 PM | 1:00 PM | 8:00 AM | 10:00 PM |
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July 25, 2022
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7:45 to 8:00 pm
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Opening remarks
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8:00 to 8:50 pm
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Areejit Samal “Forman-Ricci
curvature: A geometry-inspired measure with wide applications in network
science”
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8:50 to 9:40 pm
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Jie Wu “Topological
Approaches to Graph Data”
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9:40 to 10:00 pm
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20-minute break
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10:00 to 10:50 pm
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Chandrajit Bajaj “Learning
Optimal Control with Stochastic Models of Hamiltonian Dynamics for Shape and
Function Optimization”
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10:50 to 11:40 pm
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Christian Kuehn “Dynamical
Systems for Deep Neural Networks”
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July 26, 2022
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2:00 to 2:50 pm
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Jia-Kun Liu “Some
applications of optimal transportation”
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2:50 to 3:40 pm
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Hong Van Le Prague “Supervised
learning with probabilistic morphisms and kernel mean embedding”
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3:40 to 4:00 pm
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20-minute break
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4:00 to 4:50 pm
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Norbert Peyerimhoff “A
curvature flow for weighted graphs based on the Bakry-Emery calculus”
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4:50 to 5:40 pm
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Hao Xu “Frobenius
algebra structure of statistical manifold”
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July 27, 2022
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8:00 to 8:50 am
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Bobo Hua “Curvature conditions on graphs”
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8:50 to 9:40 am
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Alexander Strang “A
Functional Theory for Principal Trade-off Analysis”
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9:40 to 10:00 am
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20-minute break
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10:00 to 10:50 am
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Junjie Wee “Mathematical
AI for Molecular Sciences”
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10:50 to 11:40 am
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Mustafa Hajij “A
unifying deep learning framework with higher order attention networks”
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2:00 to 2:50 pm
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Konrad Polthier “Boundary-sensitive
Hodge decompositions”
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2:50 to 3:40 pm
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Parvaneh Joharinad “Curvature
of Data”
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3:40 to 4:00 pm
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20-minute
break
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4:00 to 4:50 pm
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Dong Zhang “Higher
order eigenvalues for graph p-Laplacians”
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4:50 to 5:40 pm
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Shiping Liu “Signed
graphs and Nodal domain theorems for symmetric matrices”
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July 28, 2022
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2:00 to 2:50 pm
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Shi-Bing Chen “The
optimal partial transport problem”
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2:50 to 3:40 pm
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Alexander Bobenko "The Bonnet problem: Is a surface characterized by its metric and curvatures?"
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3:40 to 4:00 pm
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20-minute
break
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4:00 to 4:50 pm
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Mathieu Desbrun “Connection-based Dimensionality
Reduction”
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4:50 to 5:40 pm
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Michael Farber “Algorithms for automated decision
making and topology”
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July 29, 2022
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2:00 to 2:50 pm
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Emil Saucan “Discrete
Morse Theory, Persistent Homology and Forman-Ricci Curvature”
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2:50 to 3:40 pm
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Marzieh Eidi “Seeing Data Through the Lens of
Geometry (Ollivier-Ricci Curvature)”
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3:40 to 4:00 pm
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20-minute
break
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4:00 to 4:50 pm
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Ye Ke “Geometry of the
convergence analysis for low rank partially orthogonal tensor approximation
problem”
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4:50 to 5:40 pm
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Anna Wienhard “Graph
Embeddings in Symmetric Spaces”
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Zoom information:
Zoom link: https://us06web.zoom.us/j/82596487514?pwd=azc4MC83NFpZUmhrcjZ1RmphM3B3dz09
Zoom account: 825 9648 7514
Password: 202207
Recorded videos on youtube: https://www.youtube.com/watch?v=KNdlXb53FbE&list=PL4kY-dS_mSmKrWXbhmxmuq3OkvioLmX2T&ab_channel=MathematicalAIforMolecularSciences
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