1<HTML> 2<body background=rocks2.jpg> 3 4 5<body topmargin="50"> 6<body leftmargin="50"> 7 8 9<meta name="viewport" content="width=device-width, initial-scale=1.0"> 10<link rel="stylesheet" type="text/css" href="style.css"> 11 12 13<div class="topnav" id="myTopnav"> 14 <a href="index.html">Home</a> 15 <div class="dropdown"><button class="dropbtn">Research<i class="fa fa-caret-down"></i></button> 16 <div class="dropdown-content"> 17 <a href="research.html">Papers</a> 18 <a href="talks.html">Talks and notes</a> 19 <a href="research.html#software">Software</a> 20 </div> 21 </div> 22<a href="teaching.html">Teaching</a> 23<a href=cv.pdf>CV</a> 24 <div class="dropdown"><button class="dropbtn">Conferences and Seminars<i class="fa fa-caret-down"></i></button> 25 <div class="dropdown-content"> 26 <a href="organization.html">Things I organize</a> 27 <a href=champ/index.html>CHAMP</a> 28 <a href=https://nebraskacommalg.github.io/RTG/conferences/reu.html>International REU</a> 29 <a href=https://nebraskacommalg.github.io/RTG/seminar.html>UNL Commutative Algebra Seminar</a> 30 <a href=https://eloisagrifo.github.io/conferences/camp.html>Summer CAMP</a> 31 <a href=https://eloisagrifo.github.io/conferences/bhargav.html>Commutative algebra in mixed characteristic</a> 32 </div> 33 </div> 34 <a href="javascript:void(0);" class="icon" onclick="myFunction()">☰</a> 35</div> 36 37 38
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49 50 51 52 53<head> 54 <TITLE> 55 Eloísa Grifo | Talk notes 56 </TITLE> 57 <LINK REV="made" HREF="mailto:grifo@unl.edu"> 58 59 </HEAD> 60 61 62 63 64<h2><center>Notes on symbolic powers</center></h2> 65 66 67Here is video of a talk on symbolic powers I gave at the <a href=https://sites.google.com/view/fellowship-of-the-ring/>Fellowship of the ring</a>, the virtual Worldwide Commutative Algebra Seminar, hosted by MSRI. 68<br> 69<br> 70<center> 71<iframe width="560" height="315" src="https://www.youtube.com/embed/Be83xC1isy4" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> 72</center> 73<br> 74<br> 75 76 77 78 79I've written several sets of lecture notes on symbolic powers. All of these are drafts and are highly likely to contain typos. 80 81 82 83 84<br><br> 85 86<b>Notes directed at advanced commutative algebra graduate students:</b> 87<br> 88The following are notes I wrote for a semester long course on symbolic powers at the University of Nebrask—Lincoln: 89<br><br> 90<center><a href=SymbolicPowers.pdf>Main symbolic powers notes</a></center> 91<br> 92These are likely to still contain typos, but these are the most up-to-date notes I have written on the subject. 93<br><br> 94I have also written shorter notes for week-long courses. The notes below were written for the <a href=http://ac2019.eventos.cimat.mx>Escuela de otoño de Àlgebra Conmutativa</a> at <a href=https://www.cimat.mx>CIMAT</a> in November 2019 organized by <a href="http://www.cimat.mx/~luisnub/home.html">Luis Núñez-Betancourt</a> and <a href=http://personal.cimat.mx:8181/~abraham.mc/Home.html>Abraham Martín del Campo</a>, and earlier for the <a href="https://www.math.utah.edu/agtrtg/commutative-algebra/ 95">RTG Advanced Mini-course in Commutative Algebra</a> at the University of Utah in May 2018, organized by <a href=https://www.math.utah.edu/~singh/>Anurag K. Singh</a> and <a href=https://www.math.utah.edu/~iyengar/>Srikanth B. Iyengar</a>. The <a href="SymbolicPowersUtah.pdf">older version of my notes on symbolic powers</a> is no longer kept updated, so I'd recommend reading the newer version below. While the CIMAT lectures were delivered in spanish, the main version of the notes is the English version, and the others are more or less translations of the English version. 96 97<br><br> 98<center> 99<a href="SymbolicPowersCIMAT.pdf">english version</a> 100 101<a href="SymbolicPowersEspanol.pdf">versión en español</a> 102 103<a href="SymbolicPowersTuga.pdf">versão em português</a> 104</center> 105 106<br><br> 107 108<b>Notes directed at advanced undergraduates:</b> 109<br> 110These are the materials for the lecture series I gave at <a href=http://www.math.utah.edu/awmchapter/conference/>BRIDGES</a>, a conference aimed towards early graduate students and advanced undergraduate students interested in representation theory, number theory, and commutative algebra, hosted by the University of Utah AWM student chapter. These lectures assumed only a first course in algebra, and no commutative algebra background. 111 112<br><br> 113<center> 114<a href=bridges/bridges.pdf>Lecture notes</a> 115 116<a href=bridges/BridgesProblems.pdf>Problem list</a> 117 118<a href=bridges/bridges1.pdf>Day 1</a> 119 120<a href=bridges/bridges2.pdf>Day 2</a> 121 122<a href=bridges/bridges3.pdf>Day 3</a> 123</center> 124 125 126 127<br> 128 129<h2><center>Other videos from research talks</h2> 130 131 132 133 134<a href=https://icerm.brown.edu/video_archive/?play=2651>Symbolic powers in mixed characteristic</a>, at the ICERM workshop <a href=https://icerm.brown.edu/topical_workshops/tw-21-dmga/>D-modules, Group Actions, and Frobenius: Computing on Singularities</a> 135 136<br><br> 137 138<div class="row"> 139 <div class="column1"> 140<center> 141<br><br><br><br><br> 142<a href=Talks/OaxacaMixedChar.pdf>Symbolic powers in mixed characteristic</a> 143<br> 144in 145<br> 146<a href=https://www.birs.ca/events/2022/5-day-workshops/22w5174>BIRS workshop on advances in mixed char</a> 147<br> 148May 10, 2022 149</center> 150</div> 151<div class="column2"> 152 153<iframe width="512" height="288" src="http://www.birs.ca/events/2022/5-day-workshops/22w5174/videos/embed/202205100915-Grifo.mp4" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> 154 155</div></div> 156</li> 157 158 159<div class="row"> 160 <div class="column1"> 161<center> 162<br><br><br><br><br> 163<a href=Talks/FRGUtah2021.pdf>Symbolic powers in mixed characteristic</a> 164<br> 165in 166<br> 167<a href=https://sites.google.com/view/special-month-on-singularities/home>Special Month On Singularities & K-Stability</a> 168<br> 169June 6, 2021 170</center> 171</div> 172<div class="column2"> 173 174<iframe width="512" height="288" src="https://www.youtube.com/embed/9UUmgDbhjbc" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> 175 176</div></div> 177</li> 178 179 180<div class="row"> 181 <div class="column1"> 182<center> 183<br><br><br><br><br> 184<a href=Talks/MCA2021.pdf>Differential powers in mixed characteristic</a> 185<br> 186in 187<br> 188<a href=https://www.mca2021.org/en/special-sessions/item/55-differential-operators-in-algebraic-geometry-and-commutative-algebra>Special Session on differential operators in algebraic geometry and commutative algebra</a> at the <a href=https://www.mca2021.org/en/>2021 MCA</a> 189<br> 190July 16, 2021 191</center> 192</div> 193<div class="column2"> 194 195<iframe width="512" height="288" src="https://www.youtube.com/embed/LUWQ0zHyGY4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe> 196 197</div></div> 198</li> 199 200 201 202 203 204<br><br><br> 205 206 207 208 <H2><center> 209 Notes and slides from research talks</center> 210 </H2> 211 212 213<ul> 214 215 216<li> 217<a href=Talks/OaxacaMixedChar.pdf>Symbolic powers in mixed characteristic</a> 218 219(<a href=https://www.birs.ca/events/2022/5-day-workshops/22w5174>BIRS workshop on advances in mixed char</a>, 05/10/2022) 220<br> 221</li> 222 223 224<li> 225<a href=Talks/CA+.pdf>Cohomological Support Varieties</a> 226 227(<a href=http://www.fields.utoronto.ca/activities/21-22/CAAC2022>CA+</a> at Iowa State, 05/01/2022, and <a href=https://math.unl.edu/kumunu-2021>KUMUNU</a> at UNL, 05/08/2022) 228<br> 229</li> 230 231 232 233<li> 234<a href=Talks/CAAC2022.pdf>Symbolic powers</a> 235 236(<a href=http://www.fields.utoronto.ca/activities/21-22/CAAC2022>
236Combinatorial Algebra meets Algebraic Combinatorics</a> at the Fields Institute, 01/23/2022) 237<br> 238</li> 239 240 241<li> 242<a href=Talks/ICERM2021.pdf>Symbolic powers in mixed characteristic</a> 243 244(ICERM workshop <a href=https://icerm.brown.edu/topical_workshops/tw-21-dmga/>D-modules, Group Actions, and Frobenius: Computing on Singularities</a>, 08/12/2021) 245<br> 246</li> 247 248 249<li> 250<a href=Talks/MCA2021.pdf>Differential powers in mixed characteristic</a> 251 252(<a href=https://www.mca2021.org/en/special-sessions/item/55-differential-operators-in-algebraic-geometry-and-commutative-algebra>Special session on Differential operators in CA and AG</a> at the <a href=https://www.mca2021.org/en/>Mathematical Congress of the Americas</a>, 07/16/2021) 253<br> 254</li> 255 256 257<li> 258<a href=Talks/FRGUtah2021.pdf>Symbolic powers in mixed characteristic</a> 259 260(<a href=https://sites.google.com/view/special-month-on-singularities/home>Special Month On Singularities & K-Stability</a> 06/07/2021) 261<br> 262</li> 263 264 265<li> 266<a href=Talks/NotreDame2021.pdf>Test modules for the complete intersection property</a> 267 268(Notre Dame AG/CA Seminar 04/27/2021) 269<br> 270</li> 271 272 273<li> 274<a href=Talks/AMS2021Cincinnati.pdf>Test modules for the complete intersection property</a> 275 276(Special Session on <a href=https://www.ams.org/meetings/sectional/2286_program_ss7.html#title>Commutative Algebra</a> at the <a href=https://www.ams.org/meetings/sectional/2286_program.html>Cincinnati Virtual AMS Sectional Meeting</a>.) 277<br> 278</li> 279 280 281<li> 282<a href=Talks/AMS2021Brown.pdf>Constructing non-proxy small modules</a> 283 284(Special Session on <a href=http://www.ams.org/meetings/sectional/2284_program_ss1.html#title>Commutative Algebra</a> at the <a href=http://www.ams.org/meetings/sectional/2284_special.html>Brown Virtual AMS Sectional Meeting</a>) 285<br> 286</li> 287 288 289 290<li> 291<a href=Talks/Mulheres.pdf>Symbolic Powers</a> 292 293(Mulheres Matemáticas: uma tarde de encontro) 294<br> 295</li> 296 297 298<li> 299<a href=Talks/UNLOctober2020.pdf>Constructing non-proxy small modules</a> 300 301(UNL Commutative Algebra Seminar) 302<br> 303</li> 304 305 306<li> 307<a href=Talks/AMS2020October.pdf>Constructing non-proxy small modules</a> 308 309(<a href=http://www.ams.org/meetings/sectional/2278_program_ss5.html#title>Special Session on Homological Methods in Algebra</a> at the Virtual Fall AMS Sectional Meeting 2020) 310<br> 311</li> 312 313 314 315<li> 316<a href=Talks/FOTR.pdf>Symbolic Powers, stable containments, and degree bounds</a> 317— these notes correspond to the <a href=https://www.youtube.com/watch?v=Be83xC1isy4>video</a> above 318 319(<a href=https://www.msri.org/general_events/24976>Fellowship of the ring, worldwide seminar</a>) 320<br> 321</li> 322 323 324 325 326<li> 327<a href=Talks/SwitzerlandZoom.pdf>Symbolic Powers and the (stable) containment problem</a> 328 329(Bern/Fribourg/Neuchâtel InterCity Seminar) 330<br></li> 331 332 333 334 335<li> 336<a href=Talks/TulaneColloquium.pdf>Symbolic Powers</a> 337 338(Tulane University Colloquium) 339<br></li> 340 341 342<li> 343<a href=Talks/TulaneAlgebra.pdf>Symbolic Powers and the (stable) containment problem</a> 344 345(Tulane University Algebra and Combinatorics Seminar) 346<br></li> 347 348 349<li> 350<a href=Talks/UNLColloquium2020.pdf>Symbolic Powers</a> 351 352(University of Nebraska — Lincoln Colloquium) 353<br></li> 354 355 356<li> 357<a href=Talks/UIC2019.pdf>A stable version of Harbourne's Conjecture</a> 358 359(University of Illinois at Chicago Commutative Algebra Seminar) 360<br></li> 361 362 363<li> 364Symbolic powers and <a href=Talks/UNLCAFall2019.pdf>Two versions of Harbourne's Conjecture</a> (2 part talk) 365 366(University of Nebraska — Lincoln Commutative Algebra Seminar) 367<br></li> 368 369<li> 370<a href=Talks/UtahAugust2019.pdf>A stable version of Harbourne's Conjecture</a> 371 372(University of Utah Commutative Algebra Seminar) 373<br></li> 374 375 376<li> 377<a href=Talks/Wisconsin2019.pdf>Symbolic powers and the (stable) containment problem</a> 378 379(University of Wisconsin Madison Algebra and Algebraic Geometry Seminar) 380<br></li> 381 382 383 384<li> 385<a href=Talks/MorgantownAlgebraDays2019.pdf>A Fedder-type criterion over Gorenstein rings</a> 386 387(<a href=https://math.wvu.edu/mad2019/>Morgantown Algebra Days</a>) 388<br></li> 389 390 391 392<li> 393<a href=Talks/CentralMichiganSeminar.pdf>Symbolic powers and the containment problem</a> 394 395(Central Michigan Algebra and Combinatorics Seminar) 396<br></li> 397 398 399 400<li> 401<a href=Talks/Colloquium2019.pdf>Symbolic powers</a> 402 403(UC Riverside Colloquium and Oklahoma State Colloquium) 404<br></li> 405 406 407<li> 408<a href=Talks/OberwolfachFebruary2019.pdf>A Fedder-type criterion over Gorenstein rings and symbolic powers</a> 409 410(Oberwolfach Workshop on <A href="https://www.mfo.de/occasion/1907/www_view">Singularities and Homological Aspects of Commutative Algebra</A>) 411<br></li> 412 413 414<li> 415<a href=Talks/CMSWinter.pdf>A stable version of Harbourne's Conjecture</a> 416 417(<a href=https://cms.math.ca/Events/winter18/schedule_session#srp>Special Session on Symbolic and regular powers of ideals</a> at the CMS Winter Meeting 2018) 418<br></li> 419 420 421 422<li> 423<a href=Talks/MichiganAMSDevelopments.pdf>Symbolic powers of ideals defining F-pure rings</a> 424 425(<a href=http://www.ams.org/meetings/sectional/2259_program_ss15.html#title>Special Session on Advances in Commutative Algebra</a> at the Ann Arbor AMS Meeting 2018) 426<br></li> 427 428 429<li> 430<a href=Talks/MichiganAMSComplexity.pdf>Symbolic powers and free resolutions</a> 431 432(<a href=http://www.ams.org/meetings/sectional/2259_program_ss32.html#title>Special Session on Commutative Algebra and complexity</a> at the Ann Arbor AMS Meeting 2018) 433<br></li> 434 435 436<li> 437<a href=Talks/OberwolfachOctober2018.pdf>A stable version of Harbourne's Conjecture</a> 438 439(<a href=https://www.mfo.de/occasion/1840b/www_view>
439MFO Mini-workshop on Asymptotic invariants of homogeneous ideals</a> 2018) 440<br></li> 441 442 443 444<li> 445<a href=Talks/Kumunujr2018.pdf>Homological algebra vs symbolic powers</a> 446 447(<a href=http://www.math.unl.edu/~jpollitz2/KUMUNUJr18/>KUMUNUjr</a> 2018) 448<br></li> 449 450 451 <li> 452<a href=Talks/BostonAMS.pdf>Applying homological algebra to a problem on symbolic powers</a> 453 454(Boston AMS Meeting Special Session on Homological Methods in Commutative Algebra) 455<br></li> 456 457 458 <li> 459<a href=Talks/PortlandAMS.pdf>Symbolic powers and the containment problem</a> 460 461(<a href=http://www.ams.org/meetings/sectional/2248_program_ss5.html#title>Special Session on Commutative Algebra</a> at the Portland AMS Meeting) 462<br></li> 463 464 465 <li> 466<a href=Talks/DefenseTalk.pdf>Symbolic powers and the containment problem</a> 467 468(PhD thesis defense) 469<br></li> 470 471 472 <li> 473<a href=Talks/OhioAMS.pdf>The Zariski-Nagata theorem in mixed characteristic</a> 474 475(AMS Sectional Meeting in Ohio, <A href="http://www.ams.org/meetings/sectional/2250_program_ss18.html#title">Special Session in Commutative and Combinatorial Algebra</A>) 476<br></li> 477 478 479 <li> 480<a href=Talks/JMM2018.pdf>Symbolic powers: the Containment Problem and Harbourne's Conjecture</a> 481 482(Joint Math Meetings, <A href="http://jointmathematicsmeetings.org/meetings/national/jmm2018/2197_program_ss67.html">Special Session in Commutative Algebra in All Characteristics</A>) 483<br></li> 484 485 486 <li> 487<a href=Talks/GeorgeMason2017.pdf>Symbolic powers and differential operators</a> 488 489(George Mason University Combinatorics, Algebra and Geometry Seminar) 490<br></li> 491 492 493 494 <li> 495<a href=Talks/KUNovember2017.pdf>Symbolic powers and the Containment Problem</a> 496 497(University of Kansas Algebra Seminar) 498<br></li> 499 500 501 <li> 502<a href=Talks/SouthCarolinaNovember2017.pdf>Symbolic powers and the Containment Problem</a> (2 hour talk) 503 504(University of South Carolina Algebraic Geometry Seminar) 505<br></li> 506 507 508 <li> 509<a href=Talks/NMSUOctober2017.pdf>Symbolic powers and differential operators</a> 510 511(New Mexico State University Algebra Seminar) 512<br></li> 513 514 515 <li> 516<a href=Talks/Orlando-AMS.pdf>A stable version of Harbourne's Conjecture</a> 517 518(AMS sectional meeting in Orlando, Florida, <A href="http://www.ams.org/meetings/sectional/2246_program_ss1.html#title">Special Session on Commutative Algebra</A>) 519<br></li> 520 521 <li> 522<a href=Talks/Denton-AMS.pdf>A stable version of Harbourne's Conjecture</a> 523 524(AMS sectional meeting in Denton, Texas, <A href="http://www.ams.org/meetings/sectional/2249_program_ss10.html#title">Special Session on Commutative Algebra</A>) 525<br> 526 </li> 527 528 529 <li> 530<a href=Talks/NYC-AMS.pdf>Symbolic powers of ideals defining F-pure rings</a> 531 532(AMS sectional meeting in New York, New York, <A href="http://www.ams.org/meetings/sectional/2242_program_ss1.html#title">Special Session on Commutative Algebra</A>) 533<br> 534 </li> 535 536 537 <li> 538<a href=Talks/UtahApril2017.pdf>Symbolic powers of ideals defining F-pure rings</a> 539 540(University of Utah Commutative Algebra Seminar) 541 542 543 <li> 544<a href=Talks/SC-AMS.pdf>Symbolic powers of ideals defining F-pure rings</a> 545 546(AMS sectional meeting in Charleston, SC, <A href="http://www.ams.org/meetings/sectional/2228_program_ss1.html#title">Special Session on Commutative Algebra</A>) 547<br> 548 </li> 549 550 551 <li> 552<a href=Talks/NebraskaMarch2017.pdf>Symbolic powers in characteristic p</a> (2 hour talk) 553 554(University of Nebraska — Lincoln Commutative Algebra Seminar) 555<br></li> 556 557 558 559 560<li> 561<a href=Talks/ClemsonMarch2017.pdf>Symbolic powers</a> 562 563(Clemson University Algebra and Discrete Math Seminar) 564<br></li> 565 566 567 <li> 568<a href=Talks/MichiganJanuary2017.pdf>Symbolic powers of ideals defining F-pure rings</a> 569 570(University of Michigan Commutative Algebra Seminar) 571<br></li> 572</ul> 573 574 575<br> 576<br> 577 578 579<p align=center> 580<img src=eloisatalk2.jpeg height=250 hspace=50> 581<img src=eloisatalk3.jpeg height=250 hspace=50> 582</p> 583 584 585<br> 586<br> 587 588 589 <H2><center> 590 Notes and slides from expository talks and talks directed at undergraduates</center> 591 </H2> 592 593 594<ul> 595 596 597<li> 598<a href=Talks/UCRGrad.pdf>A story of algebra vs geometry</a> 599 600(UCR Graduate Open House, November 2020) 601<br> 602</li> 603 604 605<li> 606<a href=Talks/BIKES2020charp.pdf>Frobenius or: how I learned to stop worrying and love characteristic p</a> 607 608(BIKES, University of Utah Commutative Algebra Student Seminar, January 2020) 609<br></li> 610 611<li> 612<a href=Talks/UndergraduateSymposium.pdf>Symbolic powers and a story of algebra vs geometry</a> 613 614(<a href=https://homepages.math.uic.edu/ums/>Undergraduate Research Symposium</a>, UIC, November 2019) 615<br></li> 616 617 618<li> 619<a href=Talks/StudentCASemUM2019.pdf>Symbolic powers</a> 620 621(University of Michigan Graduate Student Commutative Algebra Seminar, Winter of 2019) 622<br></li> 623 624 625 626<li> 627<a href=Talks/UMichMathClub2019.pdf>Slicing a square pizza</a> 628 629(University of Michigan Math Club, Winter of 2019) 630<br></li> 631 632 633<li> 634<a href=Talks/SingularitiesCharp.pdf>An introduction to singularities in characteristic p: Frobenius is your friend</a> 635 636(Reading course on singularities organized by <a href=http://www-personal.umich.edu/~malloryd/>Devlin Mallory</a> at UMich in the Fall of 2018) 637<br></li> 638 639 640</ul> 641 642<br><br><br><br><br><br><br><br> 643 644<hr color=#808080> 645<p class="caption"><center> 646 email: grifo@unl.edu | Office: 339 Avery Hall 647</center> </p> 648 649 650</BODY> 651 652 653
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