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Hora Lab
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The lab studies the boundary between probability theory and the representation theory of groups, using measures as its guide.

AboutAbout the lab
Walking the boundary between probability and representation theory.
Prof. Hora studies the boundary region between probability theory and the representation theory of groups.
The guiding idea is the concept of a measure, and a tendency to take detours along the way is what gives this approach its character.
Interest centers on bridging the finite and the infinite, with limit theorems, asymptotic representation theory, and noncommutative harmonic analysis as keywords.
The current main interest is the analysis of probabilistic phenomena generated by the actions of huge groups.
Key terms
- Measure
- A way of assigning a numerical "size" to sets and shapes. Probability is one example
- Representation theory
- A field that studies abstract objects such as groups by replacing them with collections of matrices
- Limit theorem
- A theorem describing the definite form that emerges as a whole when a large number of chance events accumulate
ResearchResearch themes
The lab studies the boundary between probability theory and the representation theory of groups, using the concept of a measure as a guide. It is interested in bridging the finite and the infinite.
*Illustrative imageThe Boundary Between Probability and Representation Theory
The lab moves back and forth between probability theory and the representation theory of groups. The concept of a measure serves as the guide, and a tendency to take detours along the way is what gives this approach its character.
*Illustrative imageBridging the Finite and the Infinite
The lab is interested in bridging the finite and the infinite. The current main interest is the analysis of probabilistic phenomena generated by the actions of huge groups.
MembersFaculty
- Project ProfessorAkihito Hora
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (cropped)
- The Boundary Between Probability and Representation Theory: “FreeBurnsideGroupExp3Gens2” William E. Skeith III / CC BY 3.0 (cropped)
- Bridging the Finite and the Infinite: “2D Random Walk Trace” Purpy Pupple / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Numata) Lab): “Young tableau for partitions of number 10” Unmismoobjetivo / CC BY 4.0 (cropped)
- Related lab (Analysis Lab (Yuhei Suzuki)): “AnimSun 13” PrzemekMajewski / CC BY-SA 4.0 (cropped)
- Related lab (Kasuya Lab): “Standard contact structure r 3” Pmassot / CC BY-SA 3.0 (cropped)
- Related lab (Geometry (Nozaki) Lab): “Trefoil knot cgi” Altapedia / CC BY-SA 4.0 (cropped)
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