[Turkmath:7376] FGC-Higher Structures Seminars::Semih Ozlem::03.02.2026 at 19:00 Istanbul time

[kazimilhan.ikeda]

Değerli Matematikçiler,

3 Şubat 2026 Salı günü, saat 19:00'da, FGE-Yüksek Yapılar Seminerleri 
kapsamında yer alan konuşmanın detaylarını aşağıda bulacaksınız.
(Bu konuşmanın 1. bölümü FGE Genel Seminerleri konuşması olarak yüz yüze 
30 Ocak 2026 Cuma günü saat 13:30'da yapılmıştır.)

Saygılarımla,
İlhan İkeda

-------- Original Message --------

Dear friends,

On 03.02.2026 Tuesday, at 19:00 Istanbul local time (note the unusual 
time), Semih Ozlem from Mudanya University will be the speaker of our 
FGC Higher Structures Seminars.

The details of Semih's seminar talk are as follows:

Speaker: Semih Ozlem (Mudanya University)
Date: February 03, 2026
Time: 19:00 Istanbul local time.

Title: Weakened Axioms, Idempotent Splittings, and the Structure of 
Learning: From Algebra to AI

Abstract:
We often think of mathematics as a tower of abstractions, but it begins 
with something deeply human: the act of telling things apart. In this 
talk, I’ll explore how this simple idea—splitting and focusing—manifests 
across different fields, from linear algebra to motives to machine 
learning.

We’ll start with a basic observation: if we relax the unit axiom in a 
vector space, the scalar multiplication by 1 becomes an idempotent, 
splitting the space into what is preserved and what is annihilated. This 
splitting phenomenon appears in surprising places: in the theory of 
motives, where projectors decompose varieties; in knot theory, where 
Jones–Wenzl projectors filter diagram algebras; and in deep learning, 
where attention mechanisms focus on relevant features.

I’ll introduce the topos-theoretic model of neural networks 
(Belfiore–Bennequin) and suggest that learning difficulties like 
catastrophic forgetting and generalization gaps can be viewed as 
homotopical obstructions to achieving “nice” (fibrant) network states. 
Architectural tools like residual connections and attention can then be 
seen as learned, conditional idempotents—adaptable splitters that help 
networks organize information.

This talk is an invitation to think structurally across disciplines. I 
won’t present finished theorems, but a framework of connections that 
links motivic philosophy, categorical algebra, and the practice of 
machine learning. The goal is to start a conversation: can tools from 
pure mathematics—obstruction theory, homotopy colimits, derivators—help 
us design more robust, interpretable, and composable learning systems?

No expertise in motives, knots, or AI is required—only curiosity about 
how ideas weave together.


Feza Gursey Center for Physics and Mathematics is inviting you to a 
scheduled Zoom meeting.
Topic: Higher Structures Seminars
Time: This is a recurring meeting Meet anytime (so Zoom link will be 
active at 18:45 Istanbul LT on)

Join Zoom Meeting
https://ozyegin-edu-tr.zoom.us/j/93563904955?pwd=9xh1VJjxaaiShD7SmI0YLs3XemY1hQ.1

Meeting ID: 935 6390 4955
Passcode: 699568

Organized by Feza Gürsey Center for Physics and Mathematics.
Zoom link is kindly provided by Özyeğin University.

Feza Gürsey Fizik ve Matematik UygAr Merkezi tarafından 
düzenlenmektedir.
Zoom bağlantısı Özyeğin Üniversitesi tarafından sağlanmaktadır.

Best regards,
Ilhan