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In classical homotopy theory, graphs are treated as 1-dimensional CW complexes. But since the classical notions of continuous maps and their homotopies do not respect the discrete nature of graphs, this fails to capture the full combinatorial...

The higher-order Titchmarsh problem concerns the correlation between higher divisor functions and primes. In this talk, I will explain how to derive an asymptotic formula for this correlation in appropriate ranges, assuming the existence of a "strong...

A phase transition is a phenomenon in physics, chemistry, and other related fields where the macroscopic behavior of a system changes qualitatively when the tuning parameter (such as temperature) that governs local interactions is varied by a small...

Hierarchical percolation is a toy model for percolation on ℤd that, much like the Euclidean model, is expected to exhibit mean-field behavior in high dimensions, non-mean-field behavior in low dimensions, and mean-field behavior with logarithmic...

Given a parabolic subgroup W I of a Coxeter system ( W , S ) , the set of left cosets w W I , for I ⊆ S , w ∈ W , is well-studied. However, the set of double cosets I , J ⊆ S for I , J ⊆ S is a less studied object. I want to analyze the double cosets...

School timetabling is a complex problem in combinatorial optimization, requiring the best possible assignment of course sections to teachers, timeslots, and classrooms. For educational institutions, the Master Timetable dictates to every single...

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It is a well-known result of Harish-Chandra that most invariant distributions on real and p-adic reductive groups (e.g., Fourier transforms of orbital integrals, and characters of representations) are represented by locally integrable functions on...

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