Scott Dodelson - 1/2 Connecting Theory to Observations @IhesFr

Uploaded July 2026 | Updated September 2026, 2 weeks ago

The basis of modern observational cosmology is the CMB and galaxy surveys. These lectures will
start by giving an overview of the various surveys, and then diving into what they have done or
will do. This includes precise determination of parameters via the two-point functions and upper
limits on PNG. Then, I will provide a few examples that move beyond the two-point function,
with the examples of CMB lensing and small scale clustering in lensing and galaxy surveys. I’ll
conclude by outlining Field Level Inference as a tool that may eventually be able to map out
primordial perturbations.

Scott Dodelson (Carnegie Mellon & Chicago University)

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Find this and many more scientific videos on carmin.tv - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.

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Scott Dodelson - 1/2 Connecting Theory to Observations

$Marek Bożejko - Łukasiewicz Logic and Tsallis Entropy Connected with Free Projections in the (...) In my talk, we consider the following topics: 1. Free and C-free probability and completely positive maps. 2. Free independent projections as a model of Jozef Łukasiewicz $n$-valued logic, $n gt 2$, and also a model of continuous logic of Łukasiewicz–Tarski. 3. Main Theorem: If $q$ is a real number and $x, y$ are from interval $(0, 1)$, then the Tsallis entropy is defined as $$ T_q (x, y) = (x_1-q + y_1-q-1)^{frac{1}{1-q}} $$ Then we have: If $P$ and $Q$ are free independent in some probability space $(A, tr)$ with trace $tr$ state on $A$, and $tr(P) = x$, $tr(yQ) = y$, then $tr(P^Q) = T_0(x, y)$. If $P$ and $Q$ are Boolean independent, then $tr(P Q) = T_2(x, y)$ and relations with Dagum distributions, which are called log-logistic distributions in many statistics models. If $P$ and $Q$ are classically independent then $tr(P^Q) = T_1(x, y) = lim_{qto 1}T_S (x, y)$, as t tends to 1. Here the projection $P^Q$ is the smallest projection on the closed linear span of $Im(P)$ and $Im(Q)$. The generalizations of cases of Tsallis entropy $T_q$, for $q$ in $(0, 1)$, we will use conditionally free independent projections. 4. Remarks on the free product of quantum channels. References: 1. M. Bożejko, Positive definite functions on the free group and the noncommutative Riesz product, Boll. Un. Mat. Ital. (6) 5-A (1986), 13–21. 2. M. Bożejko, Remarks on free projections, Heidelberg Seminar 1999. 3. W. Mlotkowski, Operator-valued version of conditionally free product, Studia Math. 153:13–30, (2002). 4. M. Bożejko, Projections in free and Boolean probability with applications to J. Lukasiewicz logic, Conference on Quantum Statistics and Related Topics, Lodz, 10 pp., 2018. 5. M. Bożejko, Conditionally free probability, in Signal Proceeding and Hypercomplex Analysis, 139–147, 2019. Marek Bożejko (Wroclaw University) Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.$

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