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1. On the Moduli of Lipschitz Homology Classes

   https://doi.org/10.1007/s12220-025-01916-6  

   Kangasniemi, Ilmari; Prywes, Eden (February 2025, The Journal of Geometric Analysis)

   Abstract We define a type of modulus$$\operatorname {dMod}_p$$ ${dMod}_p$for Lipschitz surfaces based on$$L^p$$ $L^p$-integrable measurable differential forms, generalizing the vector modulus of Aikawa and Ohtsuka. We show that this modulus satisfies a homological duality theorem, where for Hölder conjugate exponents$$p, q \in (1, \infty )$$ $p,q\in (1,\infty )$, every relative Lipschitzk-homology classchas a unique dual Lipschitz$$(n-k)$$ $(n-k)$-homology class$$c'$$ $c^{\prime }$such that$$\operatorname {dMod}_p^{1/p}(c) \operatorname {dMod}_q^{1/q}(c') = 1$$ ${dMod}_p^{1/p}\left(c\right){dMod}_q^{1/q}\left(c^{\prime }\right)=1$and the Poincaré dual ofcmaps$$c'$$ $c^{\prime }$to 1. As$$\operatorname {dMod}_p$$ ${dMod}_p$is larger than the classical surface modulus$$\operatorname {Mod}_p$$ ${Mod}_p$, we immediately recover a more general version of the estimate$$\operatorname {Mod}_p^{1/p}(c) \operatorname {Mod}_q^{1/q}(c') \le 1$$ ${Mod}_p^{1/p}\left(c\right){Mod}_q^{1/q}\left(c^{\prime }\right)\le 1$, which appears in works by Freedman and He and by Lohvansuu. Our theory is formulated in the general setting of Lipschitz Riemannian manifolds, though our results appear new in the smooth setting as well. We also provide a characterization of closed and exact Sobolev forms on Lipschitz manifolds based on integration over Lipschitzk-chains. 

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2. The immersion poset on partitions

   https://doi.org/10.1007/s10801-025-01380-z  

   Johnston, Lisa; Kenepp, David; Nguyen, Evuilynn; Paul, Digjoy; Schilling, Anne; Simone, Mary_Claire; Zhou, Regina (February 2025, Journal of Algebraic Combinatorics)

   Abstract We introduce the immersion poset$$({\mathcal {P}}(n), \leqslant _I)$$ $(P\left(n\right),{⩽}_I)$on partitions, defined by$$\lambda \leqslant _I \mu $$ $\lambda {⩽}_I\mu$if and only if$$s_\mu (x_1, \ldots , x_N) - s_\lambda (x_1, \ldots , x_N)$$ $s_{\mu }(x_1,\dots ,x_N)-s_{\lambda }(x_1,\dots ,x_N)$is monomial-positive. Relations in the immersion poset determine when irreducible polynomial representations of$$GL_N({\mathbb {C}})$$ $G{L}_N\left(C\right)$form an immersion pair, as defined by Prasad and Raghunathan [7]. We develop injections$$\textsf{SSYT}(\lambda , \nu ) \hookrightarrow \textsf{SSYT}(\mu , \nu )$$ $\mathrm{SSYT}(\lambda ,\nu )\hookrightarrow \mathrm{SSYT}(\mu ,\nu )$on semistandard Young tableaux given constraints on the shape of$$\lambda $$ $\lambda$, and present results on immersion relations among hook and two column partitions. The standard immersion poset$$({\mathcal {P}}(n), \leqslant _{std})$$ $(P\left(n\right),{⩽}_{\mathrm{std}})$is a refinement of the immersion poset, defined by$$\lambda \leqslant _{std} \mu $$ $\lambda {⩽}_{\mathrm{std}}\mu$if and only if$$\lambda \leqslant _D \mu $$ $\lambda {⩽}_D\mu$in dominance order and$$f^\lambda \leqslant f^\mu $$ $f^{\lambda }⩽f^{\mu }$, where$$f^\nu $$ $f^{\nu }$is the number of standard Young tableaux of shape$$\nu $$ $\nu$. We classify maximal elements of certain shapes in the standard immersion poset using the hook length formula. Finally, we prove Schur-positivity of power sum symmetric functions on conjectured lower intervals in the immersion poset, addressing questions posed by Sundaram [12]. 

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3. A case study of SMEFT $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ effects in diboson processes: pp → W±(ℓ±ν)γ

   https://doi.org/10.1007/JHEP05(2024)223  

   Martin, Adam (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper we explorepp→W^±(ℓ^±ν)γto$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at$$ \mathcal{O}\left(1/{\Lambda}^2\right) $$ $O\left(1/{\Lambda }^2\right)$and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~$$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ $O\left(E^4/{\Lambda }^4\right)$, as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of$$ \mathcal{O}\left(1/{\Lambda}^4\right) $$ $O\left(1/{\Lambda }^4\right)$SMEFT effects consistent with U(3)⁵flavor symmetry. Additionally, we include the decay of theW^±→ ℓ^±ν, making the calculation actually$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$. As such, we are able to study the impact of non-resonant SMEFT operators, such as$$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$ $\left(L^{†}{\overline{\sigma }}^{\mu }{\tau }^{I}L\right)\left(Q^{†}{\overline{\sigma }}^{\nu }{\tau }^{I}Q\right)$B_μν, which contribute to$$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ $\overline{q}{q}^{\prime }\to {\ell }^{\pm }\mathrm{\nu \gamma }$directly and not to$$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ $\overline{q}{q}^{\prime }\to W^{\pm }\gamma$. We show several distributions to illustrate the shape differences of the different contributions. 

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4. A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures

   https://doi.org/10.1090/tran/8976  

   Livshyts, Galyna (June 2023, Transactions of the American Mathematical Society)

   We show that for any even log-concave probability measure $\mathrm{\mu <\#comment/>}$on ${\mathbb{R}}^n$, any pair of symmetric convex sets $K$and $L$, and any $\mathrm{\lambda <\#comment/>}\in <\#comment/>[0,1]$, $\mathrm{\mu <\#comment/>}\left(\right(1-<\#comment/>\mathrm{\lambda <\#comment/>})K+\mathrm{\lambda <\#comment/>}L{)}^{c_n}\ge <\#comment/>(1-<\#comment/>\mathrm{\lambda <\#comment/>}\left)\mathrm{\mu <\#comment/>}\right(K{)}^{c_n}+\mathrm{\lambda <\#comment/>}\mathrm{\mu <\#comment/>}(L{)}^{c_n},$where $c_n\ge <\#comment/>n^{-<\#comment/>4-<\#comment/>o\left(1\right)}$. This constitutes progress towards the dimensional Brunn-Minkowski conjecture (see Richard J. Gardner and Artem Zvavitch [Tran. Amer. Math. Soc. 362 (2010), pp. 5333–5353]; Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti [J. Funct. Anal. 273 (2017), pp. 1120–1139]). Moreover, our bound improves for various special classes of log-concave measures. 

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5. Steady Radiating Gravity waves: An Exponential Asymptotics Approach

   https://doi.org/10.1007/s42286-023-00081-z  

   Kataoka, Takeshi; Akylas, T. R. (January 2024, Water Waves)

   Abstract The radiation of steady surface gravity waves by a uniform stream$$U_{0}$$ $U_0$over locally confined (width$$L$$ $L$) smooth topography is analyzed based on potential flow theory. The linear solution to this classical problem is readily found by Fourier transforms, and the nonlinear response has been studied extensively by numerical methods. Here, an asymptotic analysis is made for subcritical flow$$D/\lambda > 1$$ $D/\lambda >1$in the low-Froude-number ($$F^{2} \equiv \lambda /L \ll 1$$ $F^2\equiv \lambda /L\ll 1$) limit, where$$\lambda = U_{0}^{2} /g$$ $\lambda =U_0^2/g$is the lengthscale of radiating gravity waves and$$D$$ $D$is the uniform water depth. In this regime, the downstream wave amplitude, although formally exponentially small with respect to$$F$$ $F$, is determined by a fully nonlinear mechanism even for small topography amplitude. It is argued that this mechanism controls the wave response for a broad range of flow conditions, in contrast to linear theory which has very limited validity. 

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