KANNE, Circuit Judge.

The Internal Revenue Service ("IRS") determined that Appellant Christopher Gyorgy owed approximately $100,000 in unpaid income taxes, penalties, and interest for tax years 2002 and 2003. The IRS mailed notices of his deficiencies in 2006 and 2007, including demands for payment, to the address on his most recently filed tax return. But Gyorgy no longer lived there and did not receive the notices. More than two years later, his debts were still outstanding, so the IRS filed notice of a federal tax lien on his property in an effort to collect what he owed. Gyorgy challenged the IRS's action in a collection due process ("CDP") hearing before the IRS Office of Appeals (the "Appeals Office").

The Appeals Office sustained the IRS's filing of the lien notice. Its decision rested, in part, on findings that the IRS (1) properly mailed Gyorgy's deficiency notices to his "last known address" under I.R.C. § 6212(b)(1) before filing the lien; and (2) correctly determined his underlying tax liabilities. Gyorgy appealed both determinations to the tax court, which affirmed in relevant part after a bench trial. He now appeals the tax court's judgment. We affirm.

I. BACKGROUND

A. The IRS's Collection Efforts

From 2001 through 2003, Gyorgy earned taxable income from various sources, including wages from Goodby Silverstein & Partners (an advertising agency) and interest and dividends from his investments. But he filed no federal income tax returns for those years. In fact, he neglected to file any income tax returns from tax year 2001 through at least tax year 2007. During that same period, he moved frequently, living at eight different addresses in four cities and two states.

To determine Gyorgy's tax liability for 2001, 2002, and 2003 — the years relevant to this appeal — the IRS had to rely on W-2 forms, 1099 forms, and other information submitted by third parties to create substitute returns. See I.R.C. § 6020(b). When the substitute returns revealed deficiencies for all three years, the IRS began the process of notifying Gyorgy and attempting to collect his debts.

The IRS's computer system shows that it sent notice of Gyorgy's 2001 deficiency on or shortly after March 9, 2004, to his apartment on Octavia Street in San Francisco. That was the address he had reported on his most recently filed tax return, for the 2000 tax year, and it was the most recent address in the IRS's computer system. It is unclear whether the notice was in fact mailed, but in any event Gyorgy no longer lived on Octavia Street and did not receive it. In August 2004, the IRS assessed his deficiency for tax year 2001.

The IRS had no record of any address update from Gyorgy. But the forms submitted to the IRS by third parties showed a few possible addresses. Gyorgy's 2002 W-2s listed Octavia Street as well as an address on Lee Street in Oakland, California. His W-2 and one of his 1099s for 2003 listed an address on Jean Street in Oakland. In addition, his 1099s and other forms for both years listed his business address at Goodby Silverstein in San Francisco.

On November 29, 2004, the IRS mailed a form 2797 "R-U-There" letter to Jean Street. The letter requested Gyorgy's assistance in updating IRS records. It asked him to check a box if Jean Street was his current address, or to write in another address if it was not, then sign and return the form. The IRS received no answer to its letter.

The IRS continued to use Octavia Street as Gyorgy's address. It sent a deficiency notice there for tax year 2003 on December 11, 2006, demanding payment of $68,954 in income taxes, penalties, and interest.1 Gyorgy did not receive the notice, and the postal service returned it to the IRS marked "not deliverable as addressed" and "unable to forward" with a date stamp of "12/17/06." The IRS took no further steps (at least none reflected in the record) to locate Gyorgy or to re-issue the notice after it received the returned mail. In May 2007, it assessed his deficiency for tax year 2003.

On July 30, 2007, the IRS mailed another deficiency notice to Octavia Street, this time for tax year 2002. It demanded payment of $27,621 in taxes, penalties, and interest. Again, Gyorgy did not receive the notice, and the postal service returned it to the IRS marked "attempted — not known" and "unable to forward" with a date stamp of "08/03/07." The IRS again took no further steps to locate Gyorgy or re-issue the notice. In December 2007, it assessed his deficiency for tax year 2002.

Gyorgy did not pay his debts or petition the tax court for a redetermination of his deficiencies under I.R.C. § 6213(a) (a procedure for contesting one's tax liability after the IRS issues a deficiency notice). Two years later, his debts were still outstanding, so the IRS proceeded with collection efforts. It filed a notice of federal tax lien in the recorder's office in Cook County, Illinois, in August 2009 with respect to Gyorgy's residence at 8900 Forestview Road in Evanston, where he had been living since 2008.2 By then, Gyorgy's tax liability had grown to $120,644 ($12,684 for 2001; $30,416 for 2002; and $77,544 for 2003). The IRS sent notification of the lien filing to the subject property on Forestview Road.

Gyorgy received the notice and timely requested a CDP hearing. He questioned whether the IRS had followed the necessary procedures and claimed he was not liable for the assessed taxes.

B. The Collection Due Process Hearing

The Appeals Office conducted its CDP review between 2009 and 2011. The appeals officer assigned to Gyorgy's case asked him to submit original tax returns and supporting documentation if he disagreed with the IRS's calculation of his liabilities. To aid the task, she enclosed copies of the third-party information reported to the IRS and summaries of his income for each year. But Gyorgy — who was proceeding pro se — provided no returns or other information to challenge his liability.

Nor did Gyorgy participate meaningfully in the CDP process. The appeals officer initially scheduled a telephone conference to discuss his objections, but he did not participate or timely request an alternative date. Instead, he sent a letter the day before the hearing insisting on meeting face-to-face. The appeals officer agreed to do so, but only if Gyorgy filed his overdue tax returns from 2001 through 2010 (his non-filing appears to have been habitual). He refused, so the Appeals Office based its review on the information in the administrative file.

The Appeals Office issued a notice of determination sustaining the IRS's lien notice on July 15, 2011. It concluded that the IRS "follow[ed] all legal and procedural requirements in the assessment and collection process." In particular, it found that the IRS properly issued Gyorgy's deficiency notices to Octavia Street because that was the address on his most recently filed tax return, and because he had not "clearly and concisely notified the IRS of a change of address." The Appeals Office also upheld the IRS's determination of Gyorgy's tax liabilities because, although he claimed he was not liable, he never actually challenged the agency's calculations.

Gyorgy filed a timely petition in tax court on August 15, 2011, challenging the Appeals Office's determination. See I.R.C. § 6330(d)(1); Tax Ct. R. 331(a).

C. Proceedings before the Tax Court

The tax court granted a de novo review of Gyorgy's underlying tax liability and held a bench trial on January 28, 2013. At trial, the IRS presented the deficiency notices, evidence, and testimony in support of its calculations, but Gyorgy — who was again proceeding pro se — presented no evidence and no argument on the issue of liability.

The tax court also heard testimony concerning Gyorgy's whereabouts between 2000 and 2008. He testified that he lived on Octavia Street until the spring of 2002; on Lee Street in Oakland until the spring of 2003; on Jean Street in Oakland until November 2004; in an apartment in Irvine, California, until the spring of 2005 (he could not recall the address); on Quail Bush in Irvine until the winter of 2006; in a temporary apartment on Ridge Street in Evanston, Illinois, until the spring of 2007; on Colfax Street in Evanston until the spring of 2008; and since then on Forestview Road in Evanston. He admitted, "It's hard to keep track of it all."

Gyorgy claimed that, even though he was not filing tax returns during this period, he called the IRS's 1-800 number and submitted a change-of-address form to the post office every time he moved. He also claimed he wrote one or two letters to the IRS informing it of his new addresses (though he could not recall which ones). On cross-examination he could not recall the dates or other details of any calls or letters. For example, when asked when exactly he wrote to the IRS, he said, "I don't have specific dates. It's such a blur. One [letter] here, one there, mostly through phone calls." He had no documentation to support his testimony.

The Commissioner called Debra Dufek, the appeals team manager who supervised Gyorgy's case. She testified that Octavia Street was his address of record when the IRS mailed the deficiency notices at issue, and that he did not update his address until 2009. Gyorgy did not cross-examine her. The IRS also produced verifications that it had received no returns from Gyorgy from 2001 through 2007. Gyorgy acknowledged — and admits on appeal — that he did not file tax returns for those years.

The tax court orally issued findings of fact and an opinion on January 31, 2013. It reviewed Gyorgy's tax liability de novo and all other determinations for abuse of discretion. The court vacated the lien notice as to tax year 2001 because the Commissioner was unable to produce a copy of the deficiency notice or other proof that a notice was mailed. The Commissioner did not appeal that ruling, so tax year 2001 is not at issue here.

The tax court sustained the lien notice, however, for the 2002 and 2003 tax years. It agreed with the Appeals Office that the deficiency notices for those years were validly sent to Octavia Street because Gyorgy had not notified the IRS of a new address. It also upheld the IRS's calculation of Gyorgy's 2002 and 2003 tax liabilities because he "did not forward any arguments... or present any evidence" on that issue.

The tax court entered a final decision giving effect to its bench opinion and disposing of the parties' claims on March 25, 2013. Gyorgy filed a timely motion to vacate,3 which the tax court denied on July 22, 2013. That denial reset the clock for Gyorgy to appeal the March 25 decision. See Fed. R.App. P. 13(a)(1)(B). He filed a timely notice of appeal on October 21, 2013. See I.R.C. § 7483; Fed. R.App. P. 26(a)(1)(C).

We have jurisdiction under I.R.C. § 7482(a)(1).

II. ANALYSIS

The tax court upheld the Appeals Office's determination that the IRS (1) properly mailed deficiency notices to Gyorgy's last known address before filing the lien, and (2) correctly determined his underlying tax liabilities. We find no error in the first conclusion, and we hold that Gyorgy waived any challenge to the second conclusion.4

We begin with an overview of the CDP process and the taxpayer's right to appeal. The Internal Revenue Code (the "Code") directs the Treasury Secretary — acting through the IRS — to determine, assess, and collect federal taxes. See I.R.C. §§ 6201(a), 6301. It also requires taxpayers to file returns as prescribed by the IRS. See id. § 6011(a). If the IRS finds that a person has unpaid taxes for a given year, it must notify him of the deficiency before it can collect the debt. See id. §§ 6212(a), 6213(a). Once the IRS mails notice, the taxpayer may petition the tax court to redetermine the correct amount of the deficiency. Id. §§ 6213(a), 6214(a). If he does not file a timely petition (normally within ninety days), then the deficiency "shall be assessed, and shall be paid upon notice and demand." Id. § 6213(c).

If the taxpayer does not pay, then his tax liabilities become a lien on his real and personal property. Id. § 6321. To protect the government's rights against other secured creditors with respect to the encumbered property, the IRS must generally file a notice of the tax lien with the appropriate state authority. See id. § 6323(a), (f). It must then inform the taxpayer that it filed the lien notice. Id. § 6320(a).

The taxpayer is entitled to challenge the lien in a CDP hearing before the Appeals Office, which is an independent bureau within the IRS. Id. § 6320(b). The "hearing" is informal and may consist of correspondence, telephone conversations, or in-person meetings. Treas. Reg. § 301.6330-1(d)(2), Q & A-D6; Kindred v. Comm'r, 454 F.3d 688, 691 n. 7, 695 n. 19 (7th Cir.2006). In general, the taxpayer may raise any relevant issue. I.R.C. § 6330(c)(2)(A). That includes a challenge to his underlying tax liability if he "did not receive any statutory notice of deficiency for such tax liability or did not otherwise have an opportunity to dispute such tax liability." Id. § 6330(c)(2)(B). The appeals officer must consider the issues raised by the taxpayer and verify that the IRS followed proper procedures. Id. § 6330(c)(3).

After the hearing, the Appeals Office issues a notice of determination containing its findings and conclusions. Treas. Reg. § 301.6330-1(e), Q & A-E8. If the taxpayer is dissatisfied, he can appeal the determination to the tax court. I.R.C. § 6330(d)(1). If his underlying tax liability was properly at issue in the CDP hearing, the tax court reviews that issue de novo. Goza v. Comm'r, 114 T.C. 176, 181-82 (2000). It reviews the Appeals Office's other determinations for abuse of discretion. Id.; see also Jones v. Comm'r, 338 F.3d 463, 466 (5th Cir.2003) ("In a collection due process case in which the underlying tax liability is properly at issue, the Tax Court ... reviews the underlying liability de novo and reviews the other administrative determinations for an abuse of discretion." (citing Craig v. Comm'r, 119 T.C. 252, 260 (2002))).

The tax court's decision is in turn subject to review in the appropriate court of appeals. I.R.C. § 7482(a)(1). We review tax court decisions "in the same manner and to the same extent as decisions of the district courts in civil actions tried without a jury." Id.

With this background in hand, we turn to the two issues on appeal.

A. Validity of the Deficiency Notices

Before the IRS can assess or collect a tax deficiency, it must "send notice of such deficiency to the taxpayer" under § 6212 of the Code (subject to a few exceptions that are irrelevant here). See id. §§ 6212(a), 6213(a). Gyorgy contends that the IRS violated this mandate when it mailed the deficiency notices for 2002 and 2003 to his former address on Octavia Street, and that the notices were therefore invalid.

The Appeals Office disagreed and found that the IRS properly issued the notices. Because that conclusion was an administrative determination unrelated to the amount of Gyorgy's tax liability, the tax court's standard of review was abuse of discretion. Goza, 114 T.C. at 182; Jones, 338 F.3d at 466. We apply that same standard on appeal. See Kindred, 454 F.3d at 694; Williams v. Comm'r, 718 F.3d 89, 91-92 (2d Cir.2013) (per curiam). Accordingly, our review is "highly deferential." Kindred, 454 F.3d at 694 n. 16.

Judicial review of an administrative decision is ordinarily confined to the record that was before the agency. Fla. Power & Light Co. v. Lorion, 470 U.S. 729, 743-44, 105 S.Ct. 1598, 84 L.Ed.2d 643 (1985); Cronin v. U.S. Dept. of Agric., 919 F.2d 439, 443-44 (7th Cir.1990). But the tax court here looked beyond the CDP record when it considered trial testimony regarding the deficiency notices and Gyorgy's addresses. Whether it was appropriate for the tax court to consider that additional evidence — either because it was not bound by the administrative-record rule or because one of the exceptions to that rule applied — is a question we need not decide today because neither party objects to the tax court's expansion of the record.5 Accordingly, we will consider both the CDP record and the evidence adduced at trial in deciding whether the Appeals Office abused its discretion.

Gyorgy's main complaint is that he did not receive the deficiency notices at issue. But that does not render them invalid, for nothing in § 6212 requires actual notice. Rappaport v. United States, 583 F.2d 298, 301 (7th Cir.1978) (per curiam). On the contrary, subpart (b)(1) provides that a deficiency notice "shall be sufficient" if it is "mailed to the taxpayer at his last known address." I.R.C. § 6212(b)(1). This rule gives the IRS a "safe harbor" by permitting constructive notice where, for instance, the taxpayer has "failed to inform the Service of a change of address." Borgman v. Comm'r, 888 F.2d 916, 917 (1st Cir.1989). Congress was concerned that requiring actual notice in such cases would impose an almost impossible burden on the IRS to keep track of every taxpayer's whereabouts. See Gaw v. Comm'r, 45 F.3d 461, 465 (D.C.Cir. 1995) (discussing the legislative history of the last-known-address rule), nonacq., 1996-1 C.B. 1, 1996-2 C.B. 1; Lewis v. Comm'r, 72 T.C.M. (CCH) 790, 792 (1996) (same); H.R.Rep. No. 70-2, at 22 (1927) ("It is obviously impossible for the Commissioner to keep an up-to-date record of taxpayers' addresses."); S.Rep. No. 70-960, at 30 (1928) (same).

The last-known-address rule Congress adopted "provides a method of notification which insures that the vast majority of taxpayers will be informed that a tax deficiency has been determined against them." Jones v. United States, 889 F.2d 1448, 1450 (5th Cir.1989). The vast majority, but not all: as Gyorgy points out, a taxpayer who no longer lives at his last known address likely will not receive notice and will therefore miss his opportunity to petition the tax court for a redetermination under I.R.C. § 6213(a) (requiring the filing of a petition within ninety days after notice is mailed). But such taxpayers have other avenues to contest their liability. They can, for example, raise liability in a CDP hearing, see I.R.C. § 6330(c)(2)(B), seek an audit reconsideration, see Tucker v. Comm'r, 135 T.C. 114, 148 (2010), aff'd, 676 F.3d 1129 (D.C.Cir.2012), or pay the tax and then seek a refund, see I.R.C. § 7422(a); 28 U.S.C. § 1346(a)(1). Or, of course, they can avoid the problem in the first place by keeping the IRS informed of their current address. See Goulding v. United States, 929 F.2d 329, 331 (7th Cir. 1991) (holding that the taxpayer bore responsibility to notify the IRS of a different address).

The determinative question, then, is not whether Gyorgy received the deficiency notices for 2002 and 2003 (he did not), but whether the IRS mailed them to his "last known address" under § 6212(b)(1). To decide that question, we first discuss the governing definition of "last known address" and then apply it to this case.

1. Definition of "Last Known Address"

In numerous places — not just § 6212(b)(1) — the Code authorizes or requires the IRS to send notice to a taxpayer's "last known address."6 But the Code itself does not define that phrase, and for many years neither did the implementing regulations. So the task of construing "last known address" was left to the courts.

In Eschweiler v. United States and earlier decisions, we defined it as the address "where `the Commissioner reasonably believes the taxpayer wished to be reached at the time the notice of deficiency was sent.'" 946 F.2d 45, 48 (7th Cir.1991) (per curiam) (quoting Goulding, 929 F.2d at 331); see also McPartlin v. Comm'r, 653 F.2d 1185, 1189 (7th Cir.1981) (endorsing the tax court's definition: the "last permanent address of a definite duration to which the taxpayer has directed the Commissioner to send all communications" (internal quotation marks and citation omitted)). We held that "the IRS need only exercise reasonable diligence" under the particular circumstances of each case to determine the taxpayer's last known address. Eschweiler, 946 F.2d at 48 (citing Eschweiler v. United States, 877 F.2d 634, 636 (7th Cir.1989)).

In discharging its duty of reasonable diligence, we allowed the IRS to "rely on the address found in the return being audited, unless there is clear and concise notification from the taxpayer directing the Commissioner to use a different address." Eschweiler, 946 F.2d at 48 (internal quotation marks and citation omitted). This rule placed the burden on the taxpayer to notify the IRS of a change of address. Id. Other circuits adopted similar rules, with some differences in the exact formulation. See id. at 48 n. 5.

Ten years after Eschweiler, the Treasury Secretary promulgated a new regulation defining "last known address" wherever that phrase appears in the Code. See 66 Fed.Reg. 2817 (Jan. 12, 2001) (notice of final rulemaking). Treasury Regulation § 301.6212-2, entitled "Definition of last known address," provides in relevant part:

The last-known-address inquiry under § 301.6212-2 focuses on the information that was in the IRS's possession at the time it mailed the deficiency notice at issue. See I.R.C. § 6212(b)(1) (making notice sufficient "if mailed to the ... last known address") (emphasis added); Treas. Reg. § 301.6212-2(a) (focusing on the information the IRS "is given"); Eschweiler, 946 F.2d at 48.

Under subpart (a) of the regulation, a taxpayer's last known address is presumptively the one shown on his most recently filed and processed tax return. To update his address, the taxpayer must file a new return or give the IRS "clear and concise notification." Thus, as under our prior case law, see Eschweiler, 946 F.2d at 48, it is the taxpayer's responsibility to properly notify the IRS if he wants correspondence sent to an address other than the one on file. The revenue procedures in effect when the IRS issued Gyorgy's deficiency notices permitted notification either in writing — through a signed statement, a response to certain correspondence from the IRS, or the IRS's change-of-address form — or by oral statement directly to an IRS employee who initiated contact with the taxpayer. See Rev. Proc. 2001-18 § 5.04-05, 2001-1 C.B. 708 (effective Feb. 20, 2001), superseded by Rev. Proc. 2010-16, 2010-1 C.B. 664 (effective June 1, 2010). Additionally, subpart (b)(2) of the regulation treats a new address in the postal service's NCOA database as sufficient notification.

Other than information in the NCOA database, however, a new address obtained from a payer or another third party does not count as clear and concise notification. Treas. Reg. § 301.6212-2(b)(1). This rule is consistent with our prior decisions allowing the IRS to rely on the documents submitted by the taxpayer. See, e.g., Eschweiler, 946 F.2d at 49; see also Greenstein v. Comm'r, 60 T.C.M. (CCH) 379, 382 (1990) (holding that forms submitted by third parties "[did] not provide sufficient notification of an address change"). Indeed, because notice sent to a temporary or unverified address may be ineffective, "the IRS would run a risk in relying on address information about a taxpayer submitted by a third party." Gille v. United States, 33 F.3d 46, 48 (10th Cir.1994). If the deficiency notice is invalid, the IRS's tax assessment is generally unenforceable. See I.R.C. § 6213(a). And if the normally applicable three-year statute of limitations has expired, see id. § 6501(a), the IRS may be unable to collect the taxes at all.

Neither party here contends that § 301.6212-2 exceeds the Treasury Secretary's authority to "prescribe all needful rules and regulations for the enforcement of [the Code]," I.R.C. § 7805(a), or that it is otherwise invalid. So for purposes of this decision we accept the regulation as controlling under Chevron U.S.A. Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 843-45, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). See Stoops v. One Call Commc'ns, Inc., 141 F.3d 309, 311 (7th Cir.1998) (accepting regulations as controlling where neither party challenged their propriety). In other words, we look to § 301.6212-2 for the governing definition of "last known address." Cf. Planes v. United States, No. 8:05-CV-1242, 2006 U.S. Dist. LEXIS 72407, at *13 (M.D.Fla. Oct. 4, 2006) (following Treas. Reg. § 301.6212-2), aff'd per curiam, 239 Fed. Appx. 480 (11th Cir.2007); Lewis v. Comm'r, 98 T.C.M. (CCH) 174, 176 (2009) (same). Because our pre-2001 judicial definition of "last known address" is consistent with § 301.6212-2, however, we also continue to follow our earlier cases.7

2. Gyorgy's Last Known Address

In this case, we must decide whether the Appeals Office correctly concluded that Octavia Street was Gyorgy's last known address when the IRS mailed his deficiency notices for tax years 2002 and 2003.

The IRS sent the first notice (for 2003) in December 2006 and the second (for 2002) in July 2007. It is undisputed that, at that time, Gyorgy's most recently filed return was for tax year 2000, as he had not filed any subsequent returns. Because his 2000 return listed Octavia Street as his address, that was presumptively his last known address. See Treas. Reg. § 301.6212-2(a).

Gyorgy maintains, however, that Octavia Street was not his last known address — although he does not say which one of his addresses the IRS should have used instead. As best we can discern (his briefs are unclear), Gyorgy offers three arguments for his position.

First, he claims that although he did not file any new returns, he updated his address in other ways. The Appeals Office rejected this contention. It found that the IRS had no more recent address on file and that the postal service, having returned the two deficiency notices as "unable to forward," could not provide a more current address either. During the tax court trial, Gyorgy testified that each time he moved he left his new address with both the post office and the IRS. But he remembered few details and had no documentation to support his testimony. The IRS, by contrast, confirmed through Ms. Dufek's testimony and print-outs of the information in its computer systems that it had no record of a new address for Gyorgy until 2009. On this record, we find no error in the Appeals Office's conclusion that he did not update his address with either the IRS or the postal service before the issuance of his deficiency notices.8

Second, Gyorgy points to the fact that the W-2 and 1099 forms reported to the IRS by third parties for tax years 2002 and 2003 listed possible addresses other than Octavia Street. But new address information obtained from a third-party payer is not "clear and concise notification." Treas. Reg. § 301.6212-2(b)(1). These were only possible, not known, addresses; if Gyorgy wanted the IRS to use one of them, it was his responsibility to inform it which address was correct. See Goulding, 929 F.2d at 331; cf. Marks v. Comm'r, 947 F.2d 983, 986 (D.C.Cir.1991) (per curiam) ("[T]he Commissioner had no duty to send duplicate notices to every single address of which he had knowledge, especially when he had no reason to believe that any such address was permanent.").

In any event, the IRS attempted to verify Gyorgy's address by sending the so-called R-U-There letter in 2004 to the Jean Street residence listed on his most recent W-2. The IRS received no response. Far from demonstrating that Gyorgy had updated his address, as he argues, the R-U-There letter shows that the IRS was unable to determine whether Jean Street was his current address. It had no clear and concise notification of any address other than Octavia Street.

Gyorgy's third argument is that the IRS should have known he no longer lived on Octavia Street because the postal service returned both deficiency notices as undeliverable. That argument fails with respect to the first deficiency notice because the last-known-address inquiry focuses on the information the IRS possessed at the time of mailing. Eschweiler, 946 F.2d at 48. Once the IRS sends notice to what is at that time the last known address, as it did here, "`nothing in [section 6212] suggests that the IRS is obligated to take additional steps to effectuate delivery if the notice is returned ....'" Id. at 49-50 (quoting King v. Comm'r, 857 F.2d 676, 681 (9th Cir.1988)) (alteration in original).

But the second deficiency notice stands on different ground, according to Gyorgy. He points out that before the IRS mailed the second notice in July 2007, the postal service had already returned the first notice as undeliverable on December 17, 2006.9 At that point the IRS knew or should have known that Octavia Street was no longer Gyorgy's correct address; therefore, he argues, it was not entitled to send the second notice there. As we have already discussed, however, the IRS did not have a more recent, reliable address for Gyorgy in its files. He suggests that it should have done more to find him through its own investigation. We disagree.

To be sure, Gyorgy is correct that the IRS must use reasonable diligence to determine which address is the last known address under the applicable definition. See, e.g., Eschweiler, 946 F.2d at 48; Downing v. Comm'r, 94 T.C.M. (CCH) 319, 324 (2007). Courts have held, for example, that the IRS must carefully process and review more recent tax returns for a new address. See, e.g., McPartlin, 653 F.2d at 1190, 1193 (finding an IRS deficiency notice sent to taxpayers' old address invalid where, among other facts, they had submitted a more recent return disclosing a new address and another IRS service center had previously sent mail to the new address); Wallin v. Comm'r, 744 F.2d 674, 676-77 (9th Cir.1984) (holding that the IRS was insufficiently diligent where it knew taxpayer had moved and where a thorough computer search for her social security number would have revealed that she filed, under her new last name, a more recent joint return listing her new address).

Reasonable diligence also requires the IRS to carefully determine whether the taxpayer has otherwise provided proper notification of an address change. See, e.g., Ward v. Comm'r, 907 F.2d 517, 522 (5th Cir.1990) (holding that the IRS should have seen a "PN" notification in its computer systems indicating that a change of address was pending based on a letter from the taxpayer). And, having determined the proper address, the IRS must correctly transcribe it on the mailing envelope. See, e.g., Mulvania v. Comm'r, 769 F.2d 1376, 1377, 1379 (9th Cir.1985) (invalidating a deficiency notice which the IRS mistakenly sent to "St. Linda Isle Drive" rather than "57 Linda Isle Drive," and which the postal service returned as undeliverable).

But these cases, and other, similar cases cited by Gyorgy, do not bolster his position. As the Appeals Office correctly found, this is not a case where the IRS overlooked a more recently filed tax return, ignored an address update from the taxpayer, or misaddressed an envelope. No amount of diligence would have uncovered a new return or notification from Gyorgy because he never submitted one.

Seeking to push the IRS's reasonable-diligence obligation further, Gyorgy asks us to follow two decisions from the Fifth Circuit that required the IRS to conduct further investigation when it had reason to believe the address on file was no longer correct. In Mulder v. Commissioner, the postal service had returned two letters sent to the taxpayer's address on file, but the IRS sent a deficiency notice to that address anyway. 855 F.2d 208, 210 (5th Cir.1988). The court invalidated the notice. Id. at 212. It held that, in addition to reviewing its own files, the IRS should have inquired with the tax-preparer or the Texas motor vehicle or driver's license bureau for a new address. Id.

In Terrell v. Commissioner, the postal service had returned three letters to the taxpayer's address on file, but the IRS had not yet received notification of her new address. 625 F.3d 254, 257 (5th Cir.2010). It therefore mailed a determination denying the taxpayer's request for spousal relief to the address on file.10 Id. The notice was returned to the IRS as undeliverable. Id. Again, the Fifth Circuit invalidated the notice. Id. at 260. It explained that "[w]hen the IRS knows or should know at the time of mailing that the taxpayer's address on file may no longer be valid because of previously returned letters," it may not simply rely on the most recent address on file. Id. at 259. Instead, it must conduct "further investigation" by, for example, searching DMV records or contacting the taxpayer's employer. Id. at 259-60.

There is a tension between these two decisions and the applicable Treasury regulation, which requires a new tax return or clear and concise notification to change the last known address, see Treas. Reg. § 301.6212-2(a), and which provides that a new address obtained from a third party (other than the NCOA database) is not sufficient, see id. § 301.6212-2(b)(1). But we need not decide today whether that tension can be resolved or whether we would follow Mulder or Terrell if presented with similar facts. Even if we adopted the holdings in those cases, they would not help Gyorgy for two reasons.

First, the IRS's duty of reasonable diligence is rooted in equity. See Gaw, 45 F.3d at 468 (characterizing the duty as an "equitable obligation ... distinct from and supplementary to the statutory obligation imposed by the last known address requirements of section 6212"); 13 Mertens Law of Federal Income Taxation § 49C:16, at 2 (2015) (discussing the IRS's "equitable obligation to use reasonable diligence"). It therefore matters whether the taxpayer claiming its protection has "clean hands." See Gutierrez v. Gonzales, 458 F.3d 688, 694 (7th Cir.2006) (recognizing "the venerable doctrine that `he who comes into equity must come with clean hands'" (citation omitted)); McPartlin, 653 F.2d at 1191 (according significance to the fact that taxpayers were innocent, having done nothing to conceal their new address from the IRS).

The taxpayer in Mulder made no attempt to obscure his whereabouts. On the contrary, he notified the IRS of his new address before it sent his deficiency notice, but the IRS apparently did not process the new information in time. 855 F.2d at 211 n. 5. The taxpayer in Terrell, too, was innocent. She filed her tax returns on time, but the IRS happened to send the notice at issue several days before it received her new return reflecting a new address. 625 F.3d at 257.

Gyorgy, by contrast, neglected to file his tax returns year after year, moved frequently, and left the IRS in the dark concerning his whereabouts. This case is more like the scenario before the Tenth Circuit in Gille, where the taxpayer had not filed tax returns for several years. 33 F.3d at 47. The IRS prepared a substitute return in 1987 for tax year 1983 and sent a deficiency notice to the address listed on the last return filed by the taxpayer, for tax year 1982. Id. The postal service had already returned a letter sent to that address as undeliverable, but the IRS lacked notice of a new address. Id. at 47-48. The IRS sent four more mailings, including the deficiency notice itself, to the address on file, and the postal service returned them. Id. at 47. Yet the Tenth Circuit upheld the validity of the deficiency notice. Id. at 48. "Under these circumstances," it explained, "taxpayer, who did not bother to file a tax return after 1982, will not now be heard to complain that the IRS was not adequately diligent in its efforts to track him down." Id.

We reached a similar conclusion in Eschweiler, where the taxpayer had gone roughly four years without filing a tax return. 946 F.2d at 47 n. 3. Although the IRS knew before it sent his deficiency notice that the taxpayer's lease at the address on file had expired, id. at 47, we rejected the notion that this knowledge gave rise to "a duty of greater diligence," id. at 49 n. 6. The IRS was entitled to rely on the most recent address in its files, and the deficiency notice was valid even though the taxpayer no longer lived there. Id. at 47, 50.

The same reasoning applies here. Gyorgy is in no position to complain that the IRS should have done more to track him down. The IRS properly relied on the address listed on his most recently filed tax return.

Second, even assuming arguendo that the IRS had a duty to conduct further investigation for Gyorgy's address, he does not identify what reasonable steps it could have taken to find him. There is no evidence that the IRS had record — let alone clear and concise notification — of an address where he could have been reached in 2006 and 2007. It had already tried, to no avail, to verify the Jean Street address on his 2003 W-2. It appears, in fact, that Gyorgy did not want to be found. From 2001 through 2008, he filed no tax returns, moved seven times, never remained in the same place for more than roughly eighteen months, and often moved on after only a few months. Yet he never notified the IRS of his new addresses. The IRS cannot be expected to keep track of an itinerant taxpayer in such circumstances. See Marks, 947 F.2d at 986 ("[A] taxpayer's effort `to obscure the change in his address so as to confound the IRS' is a factor relevant in assessing whether the Commissioner acted properly." (citation omitted)).

For the reasons above, we conclude that the Appeals Office did not abuse its discretion in finding that Octavia Street was Gyorgy's last known address when the IRS mailed his deficiency notices for tax years 2002 and 2003, or in concluding that the notices were valid.

B. Gyorgy's Underlying Tax Liability

Because Gyorgy did not receive the deficiency notices at issue, he had a right to contest his underlying tax liability in his CDP hearing. See I.R.C. § 6330(c)(2)(B). He also had a right to de novo review of that issue in tax court. See Goza, 114 T.C. at 181-82. The tax court acknowledged that right and gave Gyorgy a bench trial. We normally assess de novo the tax court's legal conclusions after trial, and we review its factual findings and its applications of law to fact for clear error. Kikalos v. Comm'r, 434 F.3d 977, 981-82 (7th Cir.2006).

But here there is nothing for us to review. Gyorgy presented no arguments and no evidence before the tax court to challenge the IRS's calculation of the taxes and penalties he owes. He presented nothing before the Appeals Office either.11 After finding that the Commissioner made an adequate showing and noting the absence of any challenge from Gyorgy, the tax court upheld the IRS's determination of his liabilities for 2002 and 2003. On appeal, Gyorgy does not identify any alleged error in the tax court's decision; he has therefore waived any challenge to his tax liability. See United States v. Bryant, 750 F.3d 642, 651 (7th Cir.2014) ("Failure to develop an argument on appeal results in waiver...."); Mahaffey v. Ramos, 588 F.3d 1142, 1146 (7th Cir.2009) ("Perfunctory, undeveloped arguments without discussion or citation to pertinent legal authority are waived.").

III. CONCLUSION

We AFFIRM the judgment of the tax court.