{"title":"People are Illinois","authors":"A. Horsley, Ruquiyah Islam, D. Irwin","doi":"10.4324/9780429049538-5","DOIUrl":"https://doi.org/10.4324/9780429049538-5","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"199 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75184905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Top of Illinois","authors":"A. Horsley, Ruquiyah Islam, D. Irwin","doi":"10.4324/9780429049538-6","DOIUrl":"https://doi.org/10.4324/9780429049538-6","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73538491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Chord index for knots in thickened surfaces","authors":"Zhiyun Cheng, Hongzhu Gao, Mengjian Xu","doi":"10.1215/00192082-10188162","DOIUrl":"https://doi.org/10.1215/00192082-10188162","url":null,"abstract":"In this note, we construct a chord index homomorphism from a subgroup of H1(Σ, Z) to the group of chord indices of a knot K in Σ × I. Some knot invariants derived from this homomorphism are discussed.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45845645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On trace of Brownian motion on the boundary of a strip","authors":"Liping Li, Wenjie Sun","doi":"10.1215/00192082-9853356","DOIUrl":"https://doi.org/10.1215/00192082-9853356","url":null,"abstract":"The trace of a Markov process is the time changed process of the original process on the support of the Revuz measure used in the time change. In this paper, we will concentrate on the reflecting Brownian motions on certain closed strips. On one hand, we will formulate the concrete expression of the Dirichlet forms associated with the traces of such reflecting Brownian motions on the boundary. On the other hand, the limits of these traces as the distance between the upper and lower boundaries tends to $0$ or $infty$ will be further obtained.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45390637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luigi Ferraro, Mohsen Gheibi, David A. Jorgensen, Nicholas Packauskas, Josh Pollitz
{"title":"The homotopy Lie algebra of a Tor-independent tensor product","authors":"Luigi Ferraro, Mohsen Gheibi, David A. Jorgensen, Nicholas Packauskas, Josh Pollitz","doi":"10.1215/00192082-10592402","DOIUrl":"https://doi.org/10.1215/00192082-10592402","url":null,"abstract":"In this article we investigate a pair of surjective local ring maps $S_1leftarrow Rto S_2$ and their relation to the canonical projection $Rto S_1otimes_R S_2$, where $S_1,S_2$ are Tor-independent over $R$. Our main result asserts a structural connection between the homotopy Lie algebra of $S:=S_1otimes_R S_2$, denoted $pi(S)$, in terms of those of $R,S_1$ and $S_2$. Namely, $pi(S)$ is the pullback of (adjusted) Lie algebras along the maps $pi(S_i)to pi(R)$ in various cases, including when the maps above have residual characteristic zero. Consequences to the main theorem include structural results on Andr'{e}-Quillen cohomology, stable cohomology, and Tor algebras, as well as an equality relating the Poincar'{e} series of the common residue field of $R,S_1,S_2$ and $S$.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44000543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the multifractal analysis of measures in a probability space","authors":"Zhiming Li, B. Selmi","doi":"10.1215/00192082-9446058","DOIUrl":"https://doi.org/10.1215/00192082-9446058","url":null,"abstract":"In this paper, we calculate the relative multifractal Hausdorff and packing dimensions of measures in a probability space. Also, we obtain the analogue of Frostman’s lemma in a probability space for a relative multifractal Hausdorff measure. In the same way, there is a valid result for the relative multifractal packing pre-measure. Furthermore, we obtain the representations of the functions b and B by means of the analogue of Frostman’s lemma, and we provide a technique for showing that E is a (q,μ)-fractal with respect to ν. In addition, we suggest new proofs of theorems on the relative multifractal formalism in a probability space. They yield results even at a point q for which the multifractal functions b(q) and B(q) differ.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"65 1","pages":"687-718"},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47987815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The supercritical deformed Hermitian Yang–Mills equation on compact projective manifolds","authors":"A. Ballal","doi":"10.1215/00192082-10417484","DOIUrl":"https://doi.org/10.1215/00192082-10417484","url":null,"abstract":"In this paper, we extend a result of Gao Chen regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler manifolds to allow for the twisting function to be non-constant and slightly negative in all dimensions. Using this result, we prove that the twisted supercritical dHYM equation on compact, projective manifolds can be solved provided certain numerical conditions are satisfied.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47637820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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