1th speaker: Nguyen Bich Van, Ph.D from CMC University, Hanoi, Vietnam on ” Decomposition Theorems of Feature Spaces, Filters, and Irreducible Representations of UT\u2083(F\u2083) in Group Equivariant Convolutional Networks ”\u00a0<\/span><\/strong><\/p>\n 2nd speaker:\u00a0 Sekar Nugraheni, S.Si., M.Sc. from UGM on ” Robinson-Colombeau Ring of Generalized Numbers “<\/span><\/strong><\/p>\n Date: Wednesday, September 10, 2025<\/span><\/p>\n Time: 09.30 \u2013 12.30 WIB<\/span> Dr. Nguyen Bich Van opened her presentation by highlighting the motivation behind classical convolutional neural networks (CNNs) and the move towards their modern extension, group-equivariant convolutional neural networks (G-CNNs). She posed a central question: Why is the group UT\u2083(F\u2083) particularly useful for research in G-CNNs?<\/p>\n To address this, she reviewed several key algebraic and representation-theoretic tools, including Schur\u2019s Lemma, Maschke\u2019s Theorem, feature maps and feature spaces, equivariant convolution, convolution filters, and steerable convolutions. She emphasized the significance of equivariance in the structure of convolutional layers and its role in preserving symmetries.<\/p>\n Dr. Van then presented her main results, which included: Finally, she demonstrated how these theoretical results can be applied to design new G-CNN architectures that respect deep algebraic structures, opening potential applications in symbolic visual learning.<\/p>\n The second talk was delivered by Sekar Nugraheni, who focused on the Robinson-Colombeau Ring of Generalized Numbers. She began with a review of the non-Archimedean property and non-Archimedean fields, setting the stage for the algebraic framework of generalized numbers.<\/p>\n She then introduced the construction of R\u03c1, defined as the set of \u03c1-moderate nets (x_\u03b5) in R\u1d35 for a given directed poset I. She showed how R\u03c1 can be equipped with a ring structure through suitably defined addition and multiplication on nets.<\/p>\n Next, she introduced an equivalence relation on R\u03c1, defining the Robinson-Colombeau Ring of Generalized Numbers as the set of equivalence classes under this relation. This construction provides a rich non-Archimedean field with several interesting properties.<\/p>\n Towards the end of her talk, Sekar discussed the sharp topology on this ring, including the notions of sharply closed, sharply open, and sharply bounded sets, all generated through net-based constructions.<\/p>\n Algebra Laboratory, Department of Mathematics, FMIPA UGM\u00a0 1th speaker: Nguyen […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-347","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/comments?post=347"}],"version-history":[{"count":2,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/347\/revisions"}],"predecessor-version":[{"id":356,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/posts\/347\/revisions\/356"}],"wp:attachment":[{"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/media?parent=347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/categories?post=347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/algebra.math-ugm.id\/en\/wp-json\/wp\/v2\/tags?post=347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nLocation: Multimedia Room, Dept. of Chemistry, FMIPA UGM\/ Zoom Meeting<\/span><\/p>\n![\"\"](\"https:\/\/algebra.math-ugm.id\/wp-content\/uploads\/2025\/09\/photo_2025-09-13-21.17.46-1024x768.jpeg\")
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\n– Theorems characterizing the decomposition of equivariant feature spaces and filters.
\n– A structural preservation theorem for invariant subspace chains in G-CNNs.
\n– Explicit matrix forms of irreducible representations of UT\u2083(F\u2083).<\/p>\n![\"\"](\"https:\/\/algebra.math-ugm.id\/wp-content\/uploads\/2025\/09\/photo_2025-09-13-21.17.56-1024x773.jpeg\")
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