This Week in Mathematics


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Entries for this week: 5

Tuesday April 14, 2026

Applied and Computational Mathematics
FEMOnet & EnSF
- Kapil Chawla & Toan Huynh, Florida State University
Time: 3:05 Room: LOV 231

Thursday April 16, 2026

Financial Math
- Munawar Ali,
Time: 3.05 Room: LOV 231

Algebra seminar
Lefschetz (1,1)-theorem for singular varieties
- Ananyo Dan, CUNEF Universidad
Time: 3:05pm Room: Zoom
Abstract/Desc: Lefschetz (1,1)-theorem states that every (1,1) class in a smooth projective variety is the first Chern class of a line bundle. Such a statement fails when the variety is singular. There have been various attempts at extending the Lefschetz (1,1) to singular varieties. The most universal statement so far is due to Arapura. However, it follows from the work of Totaro that the map studied by Arapura does not look at all the possible (1,1) classes, in the singular case. Totaro suggests looking at the Bloch-Gillet-Soule cycle class map from the operational Chow group to the space of Hodge classes. In a joint work with I. Kaur, we study this map and give a criterion under which this map is surjective, thereby giving a possible Lefschetz (1,1) theorem for singular varieties. In the talk, I plan to present these results and give various examples where the surjectivity holds.

Friday April 17, 2026

Machine Learning and Data Science Seminar [url]
The Observable Wasserstein Distance
- Washington Mio, FSU
Time: 1:20 Room: Lov 106
Abstract/Desc: Calculating the Wasserstein distance between large point clouds in metric spaces is computationally costly. In Euclidean space, the sliced Wasserstein distance provides a more accessible alternative. We develop an analogue of slicing techniques for probability measures or data in metric spaces to obtain a computationally more tractable lower bound for the Wasserstein distance, a metric that we term observable Wasserstein distance. This is joint work with T. Needham, E. dos Santos, and L. Mauri.

Mathematics Colloquium [url]
From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising
- Irene Fonseca, CMU
Time: 3:05 Room: Lov 101
Abstract/Desc: What do these two themes have in common? Both are treated variationally, both deal with energies of different dimensionalities, concepts of geometric measure theory prevail in both, and higher order penalizations are considered. Will learning training schemes for choosing these penalizations in imaging may be of use in phase transitions? Phase Separation in Heterogeneous Media: Modern technologies and biological systems, such as temperature-responsive polymers and lipid rafts, take advantage of engineered inclusions, or natural heterogeneities of the medium, to obtain novel composite materials with specific physical properties. To model such situations using a variational approach based on the gradient theory of phase transitions, the potential and the wells may have to depend on the spatial position, even in a discontinuous way, and different regimes should be considered. In the critical case, where the scale of the small heterogeneities is of the same order of the scale governing the phase transition and the wells are fixed, the nteraction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. The supercritical case for fixed wells is also addressed, and in the subcritical case with moving wells, where the heterogeneities of the material are of a larger scale than that of the diffuse interface between different phases, it is observed that there is no macroscopic phase separation. Learning Training Schemes for Image Denoising: Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these systematically through multilevel approaches, for example by optimizing performance on noisy/clean image training pairs. These methods with space-dependent parameters that are piecewise constant on dyadic grids are considered, with the grid itself being part of the minimization. Improved performance on some representative test images when compared with constant optimized parameters is demonstrated.

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This Week in Mathematics