DCCG 2025 July, CalgaryDCCG 2025 July 14-18. U of Calgary, ENC 70 (Engineering Block C).https://mnaszodi.web.elte.hu/dccg2025/files/program.pdf Monday, July 141 08:159:00Registration 9:0010:00Opening 10:3011:10Deborah OliverosDeborah OliverosInstituto de Matemáticas, UNAMWe describe a new family of 3 dimensional bodies, and a unique example of a 4 dimensional body of constant width that we have called peabodies, obtained from the Reuleaux tetrahedron by replacing a small neighborhood of an envelope of spheres. This family contains, in dimension 3, the two Meissner solids and a body with tetrahedral symmetry that we have called Robert’s body. Behind this constructions lies the classical notion of confocal quadrics and conics./dccg2025/slides/Oliveros.pdf1 11:2012:00Vladyslav YaskinVladyslav YaskinUniversity of AlbertaThe homothety conjecture says that if a convex body is homothetic to one of its convex bodies of flotation, then it is an ellipsoid. We confirm this conjecture in $\mathbb R^2$ for symmetric convex bodies close to the disk. On the other hand, we show that the conjecture fails if the symmetry assumption is dropped. Joint work with M. Alfonseca, F. Nazarov, D. Ryabogin, and A. Stancu.2 14:0014:40Grigory IvanovGrigory IvanovPUC-RioThe two cornerstones of combinatorial convexity are Carathéodory’s and Helly’s theorems. These classical results have inspired a wide range of extensions and generalizations, all connecting the combinatorial structure of a family of convex sets with that of its sufficiently small subfamilies. The size of such subfamilies reflects the dimension of the ambient space. In this talk, we explore a new and rapidly developing direction: dimension-free versions of Carathéodory’s and Helly’s theorems. We will present recent results, discuss their geometric and analytic corollaries, and highlight several open problems.3 14:5015:30Deping YeDeping YeMemorial UniversityThe $\alpha$-Riesz potential and $\alpha$-Riesz energy are fundamental concepts in various areas such as physics, analysis, partial differential equations, and geometry. These notions are closely related and are used directly in defining many well-studied objects. For instance, the $\alpha$-Riesz energy can be used to derive the chord integral, a fundamental concept in integral geometry. In this talk, I will present our recent contributions concerning the first variation of the $\alpha$-Riesz energy in terms of the Asplund sum for log-concave functions. I will discuss its integral expression and the related Minkowski problem. Finally, I will provide a solution to this Minkowski problem under mild assumptions./dccg2025/slides/Ye.pdf4 15:4016:05Jaskaran KaireJaskaran KaireUniversity of ManitobaDespite recent progress on the Illumination conjecture, it remains open in general, as well as for specific classes of bodies. Bezdek, Ivanov, and Strachan showed that the conjecture holds for symmetric cap bodies in sufficiently high dimensions. Further, Ivanov and Strachan calculated the illumination number for the class of 3-dimensional centrally symmetric cap bodies to be 6. In this talk, I will show that even the broader class of all 3-dimensional cap bodies has illumination number 6. The illuminating directions can be taken to be vertices of a regular tetrahedron together with two special directions depending on the body. The proof is based on probabilistic arguments and integer linear programming. This talk is based on a joint work with A. Arman and A. Prymak./dccg2025/slides/Kaire.pdf5 16:3517:00Gyivan Eric Lopez-CamposGyivan Eric Lopez-CamposInstituto de Matemáticas, UNAMIt is well known that for every $S\in\mathbb{R}^3$, the Borsuk number of $S$ is less than or equal to $4$. In this talk, we will present a characterization of when a finite set of points in $\mathbb{R}^3$ has Borsuk number 4, as well as some applications of this fact for computing the Borsuk numbers of other kinds of structures./dccg2025/slides/LopezCampos.pdf6 17:1017:35Xia ZhouXia ZhouMemorial University of NewfoundlandAffine isoperimetric and isocapacitary inequalities are fundamental in convex geometric analysis and related fields, and play important roles in applications. This talk will focus on a higher-order extension of these inequalities in the space of real $n \times m$ matrices, $M_{n, m}(\mathbb{R})$. Several affine invariants, such as the $m$th order $p$-affine capacity, Orlicz projection bodies, and Orlicz centroid bodies, will be introduced, along with corresponding affine inequalities in the higher-order setting./dccg2025/slides/Zhou.pdf7 17:4518:25Boaz SlomkaBoaz SlomkaThe Open University of IsraelWe formulate a new analogue of Hadwiger’s illumination conjecture for complex convex bodies, along with its fractional version. We compute the illumination number of the polydisc, which plays a central role in this setting, and verify the conjectures for the classes of complex zonotopes and zonoids. Joint work with Liran Rotem and Alon Schejter/dccg2025/slides/Slomka.pdf8 19:0021:00Reception: Last Defence Lounge MacEwan Conference & Event Centre 350 MSC, 2500 University Drive NW Tuesday, July 152 9:009:40Luis MontejanoLuis MontejanoInstituto de Matemáticas UNAMIn geometry, ellipsoids play an important structural role. This is no surprise, since they are affine images of the unit ball, or, in other words, the unit balls of Hilbert spaces. Not only they are a structural and transversal part of various areas of mathematics such as functional analysis, convex geometry, affine geometry, etc., but the results about them are truly enchanting. In this talk, we will explore several of these charming geometric results./dccg2025/slides/Montejano.pdf9 10:1010:50Alexander LitvakAlexander LitvakUniversity of AlbertaWe construct an example of a non-symmetric convex body in ${\mathbb R}^n$ with a badly bounded Rademacher projection but well bounded $MM^*$. We believe that our example is interesting by itself. This is a joint work with F. Nazarov.10 11:0011:40Silvia Fernandez-MerchantSilvia Fernandez-MerchantCalifornia State University, NorthridgeIn 1982, Ungar proved that a set of $2n$ non-collinear points in the plane span at least $2n$ directions (slopes). This result is easily extendable to $2n+1$ non collinear points spanning at least $2n$ directions. These bounds are tight and the configurations achieving these minima are called direction critical. A few years later, Jamison conjectured that all large enough direction critical configurations belong to four special families. This problem can be extended to finite families of convex sets, where the directions are given by the slopes of the lines tangent to pairs of convex sets. Although there are bounds for the minimum number of directions determined by these tangent lines, a lot less is known for this variation of the problem. In this talk, we present the latest progress towards Jamison’s conjecture as well as some new results for special families of convex sets.11 11:5012:15Abraham BekeleAbraham BekeleUniversity of Missouri ColumbiaThe Klee-Wagon Conjecture on monotonicity of intersections of balls under contraction of centers states that if a collection of $k$ Euclidean balls is contracted, the volume of their intersection is non-decreasing. In this talk, we introduce a functional variant of the conjecture for intersections of randomly centered Euclidean balls. In particular, we present positive results for completely monotone functions via stochastic ordering. Joint work with Peter Pivovarov./dccg2025/slides/Bekele.pdf12 14:1514:55Balázs CsikósBalázs CsikósEötvös Loránd University, Faculty of InformaticsJordan's theorem is an important ingredient of the proof of Bieberbach's theorems on the structure of crystallographic groups in the $n$-dimensional Euclidean space. It claims the existence of a number $a(n)$ for any $n\in \mathbb N$ such that every finite subgroup $G$ of the orthogonal group $O(n)$ contains an abelian normal subgroup of index at most $a(n)$. Motivated by Jordan's theorem, Étienne Ghys conjectured that there exists a number $a(M)$ for any compact smooth manifold $M$ such that every finite subgroup $G$ of the diffeomorphism group $\mathrm{Diff}(M)$ has an abelian normal subgroup of index at most $a(M)$. The conjecture of Ghys was proved in many special cases. However, in spite of the growing expectations, it turned out that the conjecture does not hold for the product $T^2\times S^2$ of a 2-dimensional torus and a sphere. After the appearance of our counterexample Ghys revised his conjecture by replacing the word \emph{abelian} in his original conjecture by the word \emph{nilpotent}. We proved that the revised conjecture of Ghys is true not only for the diffeomorphism group of a compact smooth manifold, but also for the homeomorphism groups of compact topological manifolds. The talk reviews the results supporting the original conjecture of Ghys, the idea of the construction of the counterexample, and the main steps of the proof of the revised conjecture. (This is a joint work with László Pyber and Endre Szabó.)/dccg2025/slides/Csikos.pdf13 15:0515:45György DósaGyörgy DósaUniversity of Pannonia, Mathematical DepartmentIn this talk we consider four related square packing problems. In the first one, we try to pack $n$ squares, having sizes $1,2,\dots,n$ (one from each size) into the smallest square of size $K$ where they fit without rotation and overlap. In the second problem the issue is the opposite: with the same collection of squares we try to cover the biggest possible square (here rotation is again forbidden, but overlap is allowed). Then we consider the problem, of having squares of sizes $p,…,q$ (one from each), and having total area $K$ square for some $K$. Mullin in 1978 claimed that there is no perfect tiling for such sequences. We show that this is true for some special choices of $(p,q,K)$. It is easy to see (by computer) that there exist 126 feasible triplets in the range $1\leq p < q \leq 1000$. We prove the impossibility of about 100 cases, with various combinatorial and geometrical ideas. Finally we turn to the case $(1,24,70)$. We give the first purely combinatorial proof that the squares of sizes $1, 2,\dots, 24$ cannot fit (without overlap) into the $70\times 70$ square. So the message is the following: 70 is not enough./dccg2025/slides/Dosa.pdf14 16:1516:55Egon SchulteEgon SchulteNortheastern UniversityThe study of highly symmetric polyhedral structures in Euclidean 3-space has a long history tracing back to the early days of geometry. With the passage of time, various notions of polyhedra have attracted attention and have brought to light new exciting figures intimately related to finite or crystallographic groups of isometries. Much recent research builds on pioneering work by Coxeter and Grünbaum and focuses on skeletal polyhedra and complexes and their classification by symmetry. In this skeletal approach, a polyhedron is viewed not as a solid but rather a finite or infinite periodic geometric edge graph in space equipped with additional polyhedral super-structure imposed by the faces, and its level of symmetry is determined by distinguished transitivity properties of their geometric symmetry groups. These skeletal figures exhibit fascinating geometric, combinatorial, and algebraic properties and include many new finite and infinite structures. We discuss approaches to the classification for some of the most prominent classes of skeletal figures including the regular, chiral, or uniform polyhedra./dccg2025/slides/Schulte.pdf15 17:0517:45Greg BlekhermanGreg BlekhermanGeorgia TechIt is well known that a closed convex cone is rational polyhedral if and only if the affine semigroup of lattice points in the cone is finitely generated. The minimal set of generators is called the Hilbert basis of the cone. I will discuss the question whether the affine semigroup of lattice points in a convex cone can be finitely generated up to symmetries of the cone, with a special focus on irrational polyhedral cones.16 17:5518:20Antonio J. TorresAntonio J. TorresUC DavisIn this talk, we will discuss the slices of convex polytopes by affine hyperplanes, focusing on the sequence of possible numbers of vertices in such slices. We discuss combinatorial and geometric properties of these vertex sequences, with particular emphasis on the case of the cyclic polytopes and hypercubes.17 Wednesday, July 163 9:009:40Public Lecture by Robert ConnellyRobert ConnellyCornell UniversityIf a closed chain of fixed length is placed in a flat plane, what is the shape  that encloses the most area?  That's easy, maybe.  But what if the figure is made of bars of fixed length joined at their edges?  For example, for the 4 sided polygon in the figure, what is the shape that encloses the most area and what is that area?  Does it help to increase the area if you are allowed to decrease the length of some of the sides of the polygon? This has connections to Queen Dido of Carthage, and spiderwebs on a sphere./dccg2025/slides/Connelly.pdf18 9:5010:30Robert ConnellyRobert ConnellyCornell UniversityRecently, Martin Winter proposed that if one takes a convex polyhedron in 3-space, with the origin inside, with inextendable cables along the edges, and with incompressible struts from each vertiex to the origin, then the whole structure (called a tensegrity) is rigid.  I think of this as geodesic cabled arcs on fixed sphere.  With the idea of Part 1, it is possible to prove an interesting special case of Winter's result, but with a more global conclusion.  It has connections to ideas of the physicist James Clerk Maxwell, and polar duals of polyhedra.  The figure shows two orthogonal, but not polar duals of a rigid cabled tetrahedron on the unit sphere./dccg2025/slides/Connelly.pdf19 11:0011:40Christian BuchtaChristian BuchtaSalzburg UniversityThe convex hull of points chosen independently at random is a random polytope. Since the sixties of the last century relations between the numbers of vertices and the volumes of random polytopes have been studied. These relations turn out to be particular cases of a duality between the numbers of vertices and the volumes. The proof of the duality is based on a transformation formula for elementary symmetric polynomials. Applications in discrete mathematics are discussed./dccg2025/slides/Buchta.pdf20 11:5012:15Cameron StrachanCameron StrachanThe London School of Economics and Political ScienceIn this talk I present two results, done jointly with Konrad Swanepoel, related to an edge-isoperimetric question for Cayley graphs on the integer lattice asked by Ben Barber and Joshua Erde. For any (undirected) graph $G$, the edge boundary of a subset of vertices $S$ is the number of edges between $S$ and its complement in $G$. Barber and Erde asked whether for any Cayley graph on $\mathbb{Z}^d$, there is always an ordering of $\mathbb{Z}^d$ such that for each $n$, the first $n$ terms minimize the edge boundary among all subsets of size $n$. The first result presented answers this question in the negative by giving an example of a Cayley graph on $\mathbb{Z}^d$ (for all $d\geq 2$) for which there is no such ordering. The second result presented is a positive example of a Cayley graph on $\mathbb{Z}^2$ that has such an ordering. This is the most complicated example known to us of a two-dimensional Cayley graph for which such an ordering exists./dccg2025/slides/Strachan.pdf21 12:2512:50Zsolt LángiZsolt LángiUniversity of SzegedA convex polyhedron in $\mathbb{R}^3$ is called monostable, if it can be balanced on a horizontal plane only on one of its faces. These objects were introduced by Conway at the end of the 1960s, and were described by Shephard in 1968 as 'a remarkable class of convex polyhedra' whose properties 'it would probably be very rewarding and interesting to make a study of'. In 1969 three problems were proposed by Conway and Guy regarding monostable polyhedra, which since then were re-stated in some open problem books on geometry. In this talk we sketch the proof of these problems. Partly a joint work with Csaba D. Tóth./dccg2025/slides/Langi.pdf22 Free afternoon Thursday, July 174 9:009:40Shira ZerbibShira ZerbibIowa State UniversityWe discuss a few new results concerning convex mass partition in the plane. First we show that for any finite absolutely continuous measure in $\mathbb{R}^2$ there exists a partition of $\mathbb{R}^2$ into $2k+2$ convex parts of the same measure, such that every line misses the interior of at least $k$ parts. Moreover, the number $2k+2$ is tight if we consider only partitions with lines. This solves a special case of a problem posed by Roldán-Pensado and Soberón. We also discuss a new family of convex equipartitions of masses in the plane./dccg2025/slides/Zerbib.pdf23 10:1010:50Alina StancuAlina StancuConcordia UniversityGiven a convex body in Euclidean space, we present some constructions of convex bodies associated to K similarly with floating and illumination bodies, not all affinely invariant, and present some of their properties. (Joint work with Joao Marcondes Rodriguez)24 11:0011:40Károly J BöröczkyKároly J BöröczkyAlfred Renyi Institute of MathematicsThe first half of the talk reviews (some of the) results by Károly Bezdek on sphere packings, including his extensive oeuvre on totally separable packings. The second half of the talk discusses Maryna Viazowska's work on sphere packings in $\mathbb{R}^8$ and $\mathbb{R}^{24}$, and finally presents a stability version of her results obtained jointly with Danylo Radchenko and Joao Ramos./dccg2025/slides/Boroczky.pdf25 11:5012:15Dániel István PapváriDániel István PapváriUniversity of SzegedLet $K$ be a convex body in $\mathbb R^d$, let $j\in \{1,\ldots,d-1\}$ and let $\varrho$ be a suitable probability density function with respect to the $d$-dimensional Hausdorff measure on $K$. Denote by $K_{(n)}$ the convex hull of $n$ points chosen randomly and independently from $K$ according to the probability distribution determined by $\varrho$. For the case when $\varrho\equiv 1/V(K)$ and $\partial K$ is $C^2_+$, Reitzner (2004) proved an asymptotic formula for the expectation of the difference of the $j$th intrinsic volumes of $K$ and $K_{(n)}$, as $n\to\infty$. Böröczky, Hoffmann, and Hug (2008) extended this result to the case when $\varrho\equiv 1/V(K)$ and the only condition on $K$ is that a ball rolls freely in $K$. Böröczky, Fodor, Reitzner, and Vígh (2009) also showed that in general, the assumption of the existence of a rolling ball inside $K$, for the mean width, cannot be dropped. Böröczky, Fodor, and Hug (2010) proved an asymptotic formula for the weighted volume approximation of $K$ under no smoothness assumptions on $\partial K$. We study the expectation of weighted intrinsic volumes for random polytopes generated by non-uniform probability distributions in convex bodies with very mild smoothness conditions./dccg2025/slides/Papvari.pdf26 14:1514:55Bartlomiej ZawalskiBartlomiej ZawalskiKent State UniversityAmong all convex bodies, sections of ellipsoids and bodies of revolution exhibit particular symmetry. Namely, all hyperplanar sections of an ellipsoid are centrally symmetric and have an axis of symmetry, whereas all hyperplanar sections of a body of revolution have an axis of revolution. H. Brunn proved in 1889 that the central symmetry of all the sections characterizes ellipsoids. Much later, in 1965, C.A. Rogers observed that it is enough to consider only sections passing through a fixed point. Regarding axial symmetry, in 1999, K. Bezdek posed his celebrated conjecture that the axial symmetry of all the sections characterizes bodies of revolution in $3$-dimensional space. Now, it is natural to formulate higher-dimensional analogs of Bezdek's conjecture, and there are many ways to do it. Our main result is a proof of a certain variant of Bezdek's conjecture in arbitrary dimension $n\geq 3$, where we assume that all the sections passing through a fixed point have an axis of symmetry, satisfying certain alignment condition. Further, if we weaken the hypothesis and consider only a $1$-codimensional family of hyperplanes, we obtain a similar characterization of axially symmetric bodies. For each of these problems, we show both the orthogonal and affine variants. The talk is based on a joint work with M. Angeles Alfonseca.27 15:0515:45Beatrice-Helen VritsiouBeatrice-Helen VritsiouUniversity of AlbertaI will briefly discuss some of the history of the Hadwiger-Boltyanski illumination conjecture, and then focus on recent progress towards verifying the conjecture for 1-symmetric and 1-unconditional convex bodies./dccg2025/slides/Vritsiou.pdf28 16:1516:55Alexey GlazyrinAlexey GlazyrinThe University of Texas Rio Grande ValleyGiven a metric space $M$ and a finite set of distances $A$, we are interested in finding maximal sets of points in $M$ whose pairwise distances belong to $A$. Many problems in combinatorics and discrete geometry may be formulated in these terms. For example, the Erdős–Ko–Rado theorem provides the answer to the problem for the space of $r$-subsets of an $n$-set with $A=\{1,2,\ldots,r-1\}$; the equiangular line problem asks about the size of the maximal 1-distance set in a real projective space; etc. I will talk about the history of the problem and show several new results that work in many different settings./dccg2025/slides/Glazyrin.pdf29 17:0517:30Balázs GrünfelderBalázs GrünfelderUniversity of SzegedWe establish asymptotic upper bounds on the variances of volume and vertex number for random polytopes in non-Euclidean settings, such as spherical and hyperbolic convex bodies. Our results are obtained through two methods: one uses the gnomonic projection to reduce the problem to weighted Euclidean models, and the other provides a direct proof based on a non-Euclidean form of the economical cap covering theorem. Joint work with Ferenc Fodor./dccg2025/slides/Grunfelder.pdf30 17:4018:05Arnon ChorArnon ChorTel Aviv UniversityA flag of a polytope is a nested (w.r.t. inclusion) collection of faces of the polytope, one of each dimension. Kalai conjectured that the number of flags of a centrally symmetric polytope is minimised for the so-called Hanner polytopes (of which the cube and its dual, the cross-polytope, are the best-known examples). I will talk about a work in progress which proves this conjecture in the special case of locally anti-blocking polytopes: polytopes whose intersection with coordinate hyperplanes coincides with their projections on these hyperplanes./dccg2025/slides/Chor.pdf31 19:0021:00Conference Dinner: International House 169 University Gate NW Friday, July 185 9:009:40Peter van HintumPeter van HintumInstitute for Advanced StudyThe Prékopa-Leindler (PL) inequality serves as a functional analogue of the Brunn-Minkowski (BM) inequality on the size of sumsets in $\mathbb{R}^n$. As PL is obtained from BM as the number of dimensions tends to infinity, it can provide dimensionally independent results in the context of geometry, analysis, and probability, motivating the significant attention its stability has garnered in recent years. While a lot of progress has been made in the geometric setting of BM, a sharp quantitative stability result for the Prékopa-Leindler inequality has remained elusive. In this talk, we will explore these inequalities and present recent results that resolve the long-standing question of their quantitative stability. Special attention will also be given to the discrete aspects of these inequalities./dccg2025/slides/vanHintum.pdf32 9:5010:15Illya IvanovIllya IvanovUniversity of CalgaryA polytope is facet-lean (primitive) if removing any facet leaves an unbounded polyhedral set. I've proven that if a primitive polytope $P \subset \mathbb{E}^d$ isn't a linear image of a $d$-cube then $P$'s illumination number is strictly below $2^d$./dccg2025/slides/IvanovI.pdf33 10:5511:20Federico FirooziFederico FirooziUniversity of CalgaryThere is a remarkable and well-known enumeration result regarding lattice paths with unit up and right steps: the number of paths from $(0,0)$ to $(g,g)$ that contain $2k$ steps above the line $y=x$ does not depend on the integer~$k$. This result --- called the Chung-Feller theorem --- has inspired numerous authors to search for similar patterns throughout the years. In this accessible talk, we discuss some of our recent findings regarding paths that end at $(ga,gb)$ and respect the boundary line given by $y=\frac ba x$ for coprime integers $a,b$; these findings include a result similar to the Chung-Feller theorem and an enumeration formula that generalizes counts conducted by previous authors Grossman and Bizley. In addition to discussing these results, we explain (at a high level) the combinatorial methods we used to obtain them and reveal a connection between our formula and the study of symmetric functions. This is joint work with Jonathan Jedwab and Amarpreet Rattan./dccg2025/slides/Firoozi.pdf34 11:3011:55Ádám SagmeisterÁdám SagmeisterUniversity of SzegedProblems related to circle packings are central in discrete geometry. Here, given $n\in\mathbb{N}$, we want to find the maximum number of pairs of touching circles in a packing of $n$ congruent circles of the hyperbolic plane. It is known, that on the Euclidean plane, the extremum comes from a spiral construction of the tiling of the plane with regular triangles. Here we give both lower and upper bounds in the hyperbolic plane. In particular, we prove that if the radius of the circles is not too small, the number of touching pairs is less than the one coming from the order 7 triangular tiling. This is a joint work with Konrad Swanepoel./dccg2025/slides/Sagmeister.pdf35 12:0512:30Márton NaszódiMárton NaszódiRényi Inst. of Math. and Loránd Eötvös Univ., BudapestThe largest volume ellipsoid $E$ contained in a convex body $K$ in d-dimensional space is a central object in convexity. Fritz John gave conditions in terms of the contact points of $K$ and $E$ guaranteeing that $E$ is of largest volume. In this ongoing joint work with Grigory Ivanov, Zsolt Lángi and Ádám Sagmeister, we study the problem of finding the largest volume ellipsoid of revolution in $K$./dccg2025/slides/Naszodi.pdf36 12:4013:20Ferenc FodorFerenc FodorUniversity of SzegedThe classical Loomis--Whitney (1949) inequality provides an upper bound for the volume of a convex body via the product of the volumes of its projections to the coordinate hyperplanes. Meyer (1988) proved a lower bound on the volume using the product of the volumes of intersections with the same coordinate hyperplanes. Meyer's inequality can be regarded as a dual to the Loomis--Whitney inequality. Equality is characterized in both cases. The Bollobás--Thomason (1995) inequality is a generalization of the Loomis-Whitney inequality which also provides an upper bound for the volume via projection volumes to a suitable system of non-necessarily disjoint subspaces spanned by certain subsets of standard basis vectors. The equality case has been known as folklore. Liakopoulos (2019) proved a quite general dual statement giving a lower bound for the volume based on products of intersection volumes with certain subspaces. In the case when these subspaces are of the same types as in the Bollobás--Thomason inequality, equality was characterized by Böröczky, Kalantzopoulos and Xi (2023). We determine necessary and sufficient conditions for equality in the general case of Liakopoulos's inequality based on the recent description of the equality cases in Barthe's Reverse Geometric Brascamp--Lieb inequality. Joint work with K.J. Böröczky (Rényi Institute of Mathematics, Hungary) and P. Kalantzopoulos (University of California, Irvine, USA)./dccg2025/slides/Fodor.pdf37