Education

• Ph.D. in mathematics,Université de Lyon, Campus Jean Monnet (St-Étienne, France), Nov 2013.

• Ph.D. in electronicengineering, Università Mediterranea (Reggio di Calabria, Italy), Feb 2009.

• M.S. in electronicengineering, Università Mediterranea (Reggio di Calabria, Italy), Jan 2005.

Work Experience

• Feb 2019 topresent: associate professor of Mathematics at School of Mathematical Sciences,Hebei Normal University (Shijiazhuang, China).

• Sep - Dec 2018:visiting professor at Center for Combinatorics, Nankai University (Tianjin,China).

• Mar - 31 Aug 2018: lecturerat University of Graz (Graz, Austria).

• Mar 2016 - Feb2018: Lise Meitner research fellow at Department of Mathematics and ScientificComputing (DMSC), University of Graz (Graz, Austria).

• Nov 2015 - Feb 2016:postdoc at Centre de Mathématiques Laurent Schwartz (CMLS), École Polytechnique(Palaiseau, France).

• Nov 2014 - Oct 2015:research associate at Texas A&M University at Qatar (Doha, Qatar).

• Jan 2014 - July 2014:postdoc at Centre de Mathématiques Laurent Schwartz (CMLS), École Polytechnique(Palaiseau, France).

• May 2011 - Apr 2013: MarieCurie Intra-European research fellow at Laboratoire Jacques-Louis Lions (LJLL),Sorbonne Universités, Campus de Jussieu (Paris, France).

Publications

Preprints

• Semigroups of ideals and isomorphism problems

Pedro A. García-Sánchez and Salvatore Tringali(available upon request).

• On powermonoids and factorization

Laura Cossu and SalvatoreTringali(available upon request).

• Subcommutativity ofintegrals and quasi-arithmetic means

Dorotha Głazowska, PaoloLeonetti, Janusz Matkowski, and Salvatore Tringali

(arXiv: https://arxiv.org/abs/2305.03227).

• On power monoids and theirautomorphisms

Weihao Yan and SalvatoreTringali

(arXiv: https://arxiv.org/abs/2312.04439).

Journal papers

• On thefiniteness of certain factorization invariants

Laura Cossu andSalvatore Tringali, to appear in Arkiv för Matematik

arXiv: https://arxiv.org/abs/2301.09961

• A conjecture byBienvenu and Geroldinger on power monoids

Weihao Yan andSalvatore Tringali

to appear inProceedings of the American Mathematical Society

arXiv: https://arxiv.org/abs/2310.17713

• On the densityof sumsets, II

Paolo Leonettiand Salvatore Tringali,

to appear inBulletin Australian Mathematical Society

DOI: https://doi.org/10.1017/S000497272300062X

arXiv: https://arxiv.org/abs/2212.11176

• Factorizationunder Local Finiteness Conditions

Laura Cossu andSalvatore Tringali

Journal ofAlgebra 630 (Sept. 2023), 128-161

DOI: https://doi.org/10.1016/j.jalgebra.2023.04.014

arXiv: https://arxiv.org/abs/2208.05869

• Acharacterisation of atomicity

SalvatoreTringali

MathematicalProc. Cambridge Phil. Society 175 (2023), No. 2, 459-465

DOI: https://doi.org/10.1017/S0305004123000269

arXiv: https://arxiv.org/abs/2209.05238

• AbstractFactorization Theorems with Applications to Idempotent Factorizations

Laura Cossu andSalvatore Tringali

to appear inIsrael Journal of Mathematics

DOI: https://doi.org/10.1007/s11856-024-2623-z

arXiv: https://arxiv.org/abs/2108.12379

• An AbstractFactorization Theorem and Some Applications

SalvatoreTringali

Journal ofAlgebra 602 (July 2022), 352-380

DOI: https://doi.org/10.1016/j.jalgebra.2022.03.023

arXiv: https://arxiv.org/abs/2102.01598

• On the densityof sumsets

Paolo Leonettiand Salvatore Tringali

Monatshefte für Mathematik 198 (2022), 565-580

DOI: https://doi.org/10.1007/s00605-022-01694-1

arXiv: https://arxiv.org/abs/2001.10413

• On Small Setsof Integers

Paolo Leonettiand Salvatore Tringali

Ramanujan Journal57 (2022), 275-289

DOI: https://doi.org/10.1007/s11139-020-00371-x

arXiv: https://arxiv.org/abs/1905.08075

• On stronglyprimary monoids, with a focus on Puiseux monoids

AlfredGeroldinger, Felix Gotti, and Salvatore Tringali

Journal ofAlgebra 567 (2021), No. 1, 310-345

DOI: https://doi.org/10.1016/j.jalgebra.2020.09.019

arXiv: https://arxiv.org/abs/1910.10270

• Onhalf-factoriality of transfer Krull monoids

Weidong Gao, ChaoLiu, Salvatore Tringali, and Qinghai Zhong

Communications inAlgebra 49 (2021), No. 1, 409-420

DOI: https://doi.org/10.1080/00927872.2020.1800720

arXiv: https://arxiv.org/abs/1911.04267

• On theArithmetic of Power Monoids and Sumsets in Cyclic Groups

Austin A.Antoniou and Salvatore Tringali

Pacific Journalof Mathematics 312 (2021), No. 2, 279-308

DOI: https://doi.org/10.2140/pjm.2021.312.279

arXiv: https://arxiv.org/abs/1804.10913

• On the notionsof upper and lower density

Paolo Leonettiand Salvatore Tringali

Proc. EdinburghMathematical Society 63 (2020), No. 1, 139-167

DOI: http://dx.doi.org/10.1017/S0013091519000208

arXiv: https://arxiv.org/abs/1506.04664

• Structuralproperties of subadditive families with applications to factorization theory

SalvatoreTringali

Israel Journal ofMathematics 234 (2019), No. 1, 1-35

DOI: https://doi.org/10.1007/s11856-019-1922-2

arXiv: https://arxiv.org/abs/1706.03525

• Power monoids:A bridge between factorization theory and arithmetic combinatorics

Yushuang Fan andSalvatore Tringali

Journal ofAlgebra 512 (Oct 2018), 252-294

DOI: https://doi.org/10.1016/j.jalgebra.2018.07.010

arXiv: https://arxiv.org/abs/1701.09152

• On the numberof distinct prime factors of a sum of superpowers

Paolo Leonettiand Salvatore Tringali

Journal of NumberTheory 186 (May 2018), 226-237

DOI: https://doi.org/10.1016/j.jnt.2017.10.002

arXiv: https://arxiv.org/abs/1511.08784

• Commutativityof integral quasi-arithmetic means on measure spaces

DorothaGłazowska, Paolo Leonetti, Janusz Matkowski, and Salvatore Tringali

Acta MathematicaHungarica 153 (2017), No. 2, 350-355

DOI: https://doi.org/10.1007/s10474-017-0734-2

arXiv: https://arxiv.org/abs/1703.03938

• Arithmetic ofcommutative semigroups with a focus on semigroups of ideals and modules

Yushuang Fan,Alfred Geroldinger, Florian Kainrath, and Salvatore Tringali

Journal ofAlgebra and its Applications 16 (2017), No. 12, 1750234, 42 pp.

DOI: https://doi.org/10.1142/S0219498817502346

arXiv: https://arxiv.org/abs/1612.03116

• Upper and lowerdensities have the strong Darboux property

Paolo Leonettiand Salvatore Tringali

Journal of NumberTheory 174 (May 2017), 445-455

DOI: https://doi.org/10.1016/j.jnt.2016.11.005

arXiv: https://arxiv.org/abs/1510.07473

• MultivariateDelta Gončarov and Abel Polynomials

Rudolph Lorentz,Catherine H. Yan, and Salvatore Tringali

Journal ofMathematical Analysis and Applications 446 (2017), No. 1, 663-680

DOI: https://doi.org/10.1016/j.jmaa.2016.09.002

arXiv: https://arxiv.org/abs/1608.05836

• On thecommutation of generalized means on probability spaces

IndagationesMathematicae 27 (2016), No. 4, 945-953

Paolo Leonetti,Janusz Matkowski, and Salvatore Tringali

DOI: https://doi.org/10.1016/j.indag.2016.06.006

arXiv: https://arxiv.org/abs/1503.01139

• Sums of Dilatesin Ordered Groups

Alain Plagne andSalvatore Tringali

Communications inAlgebra 44 (2016), No. 12, 5223-5236

DOI: https://doi.org/10.1080/00927872.2016.1152476

arXiv: https://arxiv.org/abs/1403.0934

•Cauchy-Davenport type theorems for semigroups

SalvatoreTringali

Mathematika 62(2016), No. 1, 1-12

DOI: https://doi.org/10.1112/S0025579315000157

arXiv: https://arxiv.org/abs/1307.8396

• The Davenportconstant of a box

Alain Plagne andSalvatore Tringali

Acta Arithmetica171 (2015), No. 3, 197-220

DOI: https://doi.org/10.4064/aa171-3-1

arXiv: https://arxiv.org/abs/1405.4363

• Small doublingin ordered semigroups

SalvatoreTringali

Semigroup Forum90 (2015), No. 1, 135-148

DOI: https://doi.org/10.1007/s00233-014-9603-2

arXiv: https://arxiv.org/abs/1208.3233

• On a system ofequations with primes

Paolo Leonettiand Salvatore Tringali

Journal deThéories des Nombres de Bordeaux 26 (2014), No. 2, 399-413

DOI: https://doi.org/10.5802/jtnb.873

arXiv: https://arxiv.org/abs/1212.0802